Algebraic number fields

DOI10.1007/BF01093434zbMath0621.12002MaRDI QIDQ1090365

Publication date: 1987

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

survey local fields bibliography Galois theory cyclotomic fields algebraic numbers p-adic L-functions arithmetic of abelian fields Gamma-extensions reference list

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Algebraic number theory: global fields (11Rxx) Algebraic number theory: local fields (11Sxx) Homological methods (field theory) (12Gxx)

Cites Work

On units of real quadratic number fields
Unites elliptiques et unites cyclotomiques
Formulations de la conjecture de Leopoldt et étude d'une condition suffisante
The p-tower of class fields for an imaginary quadratic field
Ideals of an abelian p-extension of an irregular local field as Galois modules
On the values at rational integers of the p-adic Dirichlet L functions
Elementare Berechnung von kubischen Diskriminanten
Konstruktion von Zahlkörpern mit der Galoisgruppe $M_{11}$ über $\mathbb{Q}(\sqrt{-11})$
The distribution of the Galois groups of integral polynomials
On the adele rings and zeta-functions of algebraic number fields
On the structure of certain Galois groups
The non-p-part of the class number in a cyclotomic $\mathbb{Z}_p$-extension
Größencharaktere und Relativklassenzahl abelscher Zahlkörper
Construction of number fields with prescribed $\ell$-class groups
Embedding problem with given localizations and ramification restrictions
Zur Geschlechtertheorie algebraischer Zahlkörper
Structure of the group of principal units in a cyclic $p$-extension of a local field
Ideals of an Abelian p-extension of a local field as Galois modules
On the characterization of local fields by their absolute Galois groups
Values of the Iwasawa $L$-functions at the point $s=1$
On the genus of norm forms
Remarques sur les unites cyclotomiques et les unites elliptiques
The 2-class group of biquadratic fields. II
Polynomials with PSL(2,7) as Galois group
Representations of algebraic numbers by matrices
Gauss sums and the p-adic $\Gamma$-function
Zur Einheitenberechnung in totalreellen kubischen Zahlkörpern nach Godwin
On cyclotomic $\mathbb{Z}_2$-extensions of imaginary quadratic fields
Values at negative integers of zeta functions and $p$-adic zeta functions
Quaternionic compositum genus
On values of zeta functions and $\ell$-adic Euler characteristics
A new proof of certain formulas for p-adic L-functions
On the invariants of some $\mathbb{Z}_\ell$-extensions
Existenz unendlicher algebraischer Zahlkörper, über denen jedes Einbettungsproblem lösbar ist
A matrix criterion for normal integral bases
Sur les $l$-classes d'ideaux des extensions non galoisiennes de Q de degré premier impair $l$ à cloture galoisienne diedrale de degré 2$l$
On l-adic zeta functions
An analogue of Stickelberger's theorem for the higher K-groups
Localizability of the embedding problem with symplectic kernel
Class numbers of cubic cyclic fields
A Kronecker limit formula for real quadratic fields
Truncated units in infinitely many algebraic number fields of degree $n\geq 4$
On the $l$-class rank in some algebraic number fields
The nontriviality of certain Z$_l$-extensions
Solution of the class number two problem for cyclotomic fields
On norm maps for one dimensional formal groups. I: The cyclotomic $\Gamma$-extension
Pieces of eight in class groups of quadratic fields
Ramification in p-adic Lie extensions
Normal bases for quadratic extensions
$\Gamma$-extensions of imaginary quadratic fields
On the functional equation of the Artin L-function for characters of real representations
Lie algebras of Galois groups arising from Hodge-Tate modules
Artin-root numbers and normal integral bases for quaternion fields
New types of quadratic fields having three invariants divisible by 3
Über das Einbettungsproblem der algebraischen Zahlentheorie
An Octic Reciprocity Law of Scholz Type
Ranks of Sylow 3-subgroups of ideal class groups of certain cubic fields
The Iwasawa Invariants of Γ-Extensions of a Fixed Number Field
Local trace forms
A genus theory for quartic fields.
On the density of discriminants of quartic fields.
Dihedral extensions of Q of degree 21 which contain non-Galois extensions with class number not divisible by l
On 3-class groups of non-Galois cubic fields
On the Pythagoras number of orders in totally real number fields.
The p-Adic Gamma Measures
Über die Werte der Riemannschen Zetafunktion an den ganzzahligen Stellen.
Eine Abschätzung der Klassenzahl gewisser reiner Zahlkörper sechsten Grades.
Zur Modelltheorie Lokaler und Globaler Körper
Über die analytische Klassenzahlformel für reelle abelsche Zahlkörper.
Arithmetic euclidean rings
Adams Operations, Local Root Numbers, and the Galois Module Structure of Rings of Integers
THE NORM RESIDUE SYMBOL IN LOCAL FIELDS
GENERALIZED BERNOULLI NUMBERS AND THE BASIC ZP-EXTENSIONS OF IMAGINARY QUADRATIC NUMBER FIELDS
Structure Galoisienne Des Anneaux D'entiers
Some Remarks on Computing Galois Groups
Cyclic-Sixteen Class Fields for Q(-p) 1/2 by Modular Arithmetic
Extensions of the hasse norm theorem, II
On knots in algebraic number theory.
An analogue of Artin-Schreier theorem
$p$-adic $L$-functions for CM fields
On a certain $l$-adic representation
An abstract characterization of the Galois group of the algebraic closure of a local field
Completely solvable imbedding problems with abelian kernel for local fields
Construction of genus field and some applications
Über gewisse Galoiscohomologiegruppen
Isomorphisms of Galois groups of solvably closed Galois extensions
The admissibility of $A_5$
A note on Maus' theorem on ramification groups
Some counter-examples in the theory of the Galois module structure of wild extensions
On p-adic L-functions associated to elliptic curves
The quartic characters of certain quadratic units
A class of fundamental units and some classes of Jacobi-Perron algorithms in pure cubic fields
Representations of the Galois group and multiplicative groups of division rings over local fields
A normal integral basis theorem for dihedral groups
Some contributions to the theory of cyclic quartic extensions of the rationals
A note on the normality of unramified, Abelian extensions of quadratic extensions
Division values in local fields
Euclid's algorithm in pure quartic fields
Class groups and Brauer groups
The non-vanishing of certain Hecke $L$-functions at the center of the critical strip
Values of abelian $L$-functions at negative integers over totally real fields
Separably Hilbertian fields
Modular curves and the class group of $\mathbb{Q} (\zeta_p)$
Some invariants of $\mathbb{Z}_p^d$
Class numbers in $\mathbb{Z}_p^d$-extensions
K-théorie des anneaux d'entiers de corps de nombres et cohomologie etale
On p-adic power series
The irreducible imprimitive local Galois representations of prime dimension
Normal automorphisms of absolute Galois groups of p-adic fields
On the behavior of $p$-adic $L$-functions at $s=0$
A note on the law of decomposition of primes in certain Galois extension
The Iwasawa invariant $\mu_p$ vanishes for abelian number fields
Explizite Formeln für Einheiten algebraischer Zahlkörper und eine Familie irreduzibler Polynome über Funktionenkörpern
Applications of the theory of modular forms to number theory
On solvable number fields
On the local Langlands conjecture for central division algebras of index p
Transcendance et exponentielles en plusieurs variables
Localization of the identities of the number field
Normal basis for an ideal in a local ring
On the class number of real quadratic fields $Q(\sqrt{p})$ with p=1 (mod 4)
On the law of reciprocity in an algebraic number field
On the Stickelberger ideal and the circular units of an abelian field
Regulators and Iwasawa modules
On Fröhlich's conjecture for rings of integers of tame extensions
On the group of units of a non-galois quartic or sextic number field
On the factorization of p-adic L-series
$L$-functions at $s=1$. IV: First derivatives at $s=0$
An interpretation of the additional condition in the theory of embedding of fields with abelian kernel
Hilbert symbol in a discrete valuated field
A logarithmic approach to classgroups of integral group rings
Galois group of the maximal $\ell$-extension with a fixed ramification of the rational number field
The ring of integers of an abelian extension of an algebraic number field as a Galois module
Universally concordant Galois extensions
Another look at $p$-adic $L$-functions for totally real fields
Universal norms in Gamma-extensions
Ramification groups of infinite $p$-extensions of a local field
Units from periodic Jacobi-Perron algorithms in algebraic number fields of degree $n > 2$
On a formula of Hecke
Algebraic extensions of finite corank of Hilbertian fields
On a class number relation of imaginary Abelian fields
Über die gruppentheoretische Struktur der Relationen zwischen Relativnormabbildungen in endlichen Galoisschen Körpererweiterungen
On Cebotarev sets
On units of certain cubic number fields
Unabhängige Einheiten für die Körper $K=Q (\root n \of {D^n \pm d})$ mit $d/D^n$
Signature des unités cyclotomiques et parité du nombre de classes des extensions cycliques de $Q$ de degré premier impair
On Hilbert's irreducibility theorem
Class numbers and $\mathbb Z_p$-extensions
Extensions cubiques cycliques de $\mathbb{Q}$ dont l'anneau des entiers est monogene
On the genus field of an algebraic number field of odd prime degree
A few remarks on class numbers of imaginary quadratic number fields
On p-adic L-functions over real quadratic fields
Quadratic fields and Hopf fibrations
Exercices dyadiques
On Artin L-functions
Eine Formel für Grundeinheiten in reinen algebraischen Zahlkörpern dritten, vierten und sechsten Grades
Sommes de carrés d'entiers d'un corps $p$-adique
Der Hasse-Bernsteinsche Einheitensatz für den verallgemeinerten Jacobi- Perronschen Algorithmus
Unabhängige Einheitensysteme für eine allgemeine Klasse algebraischer Zahlkörper
A characterization of completely regular fields
Über biquadratische Zahlkörper gleicher Diskriminante
On some Galois cohomology groups of a local field and its application to the maximal p-extension
On the group automorphisms of the absolute Galois group of the rational number field
Genera in normal extensions
$L$-functions at $s=1$. II: Artin $L$-functions with rational characters
On the theory of symplectic spaces with operators
Zur Theorie der nilpotenten algebraischen Zahlkörper
Die Klassengruppen quadratischer und kubischer Zahlkörper und die Selmergruppen gewisser elliptischer Kurven
Units of modulus 1
Über die Klassenzahl gewisser nicht galoisscher Körper 6-ten Grades
Units of algebraic numberfields
Euclidean rings of algebraic numbers and functions
Prime ideal decomposition in $F({\root m\of\mu})$
Real quadratic fields with large class number
The existence of natural field structures for finite dimensional vector spaces over local fields
On the 2-part of the class number of imaginary quadratic number fields
On 3-class groups of cyclic cubic extensions of certain number fields
Completeness of the absolute Galois group of the rational number field
Isomorphisms of Galois groups
A note on p-adic L-functions
$K_i$ groups of rings of algebraic integers
Number fields with class number congruent to 4 mod 8 and Hilbert's Theorem 94
On the values at negative integers of the zeta-function of a real quadratic field
The quadratic and quartic character of certain quadratic units. I
Congruences between class numbers of quadratic number fields
Cubic fields whose class numbers are not divisible by 3
Über die Klassenzahl der Ringklassenkörper mit einem reell- quadratischen Grundkörper
Les constantes locales de l'équation fonctionnelle de la fonction L d'Artin d'une représentation orthogonale
Norms from quadratic fields and their relation to noncommuting $2\times 2$ matrices. III: A link between the 4-rank of ideal class groups in $Q(\sqrt m)$ and in $Q(\sqrt{-m})$.
Classes d'idéaux des corps abéliens et nombres de Bernoulli généralisés
A modular construction of unramified p-extensions of $\mathbb{Q}(\mu_p)$
G-closed fields and imbeddings of quadratic number fields
Über die Einheiten- und Divisorenklassengruppe von reellen Frobeniuskoerpern von Maximaltyp
On a cubic field with discriminant $163^2$
Prime ideal decomposition in $F(\mu^{1/p})$
On the Galois cohomology of Dedekind rings
Partially normal radical extensions of the rationals
The minimum discriminant of sixth degree totally complex algebraic number fields
Hilbert class fields and split extensions
Algebraic numbers, a constructive development
Iwasawa invariants of abelian number fields
Principal ideal theorems in the genus field for absolutely abelian extensions
$\mathbb{Z}_3$-invariants of real and imaginary quadratic fields
$\Gamma$-extensions of imaginary quadratic fields. II
Complete determinations of the 3-class rank in pure cubic fields
$L$-functions at $s=1$. III: Totally real fields and Hilbert's twelfth problem
Rélations entre les 2-groupes des classes d'idéaux des extensions quadratiques $k(\sqrt d)$ et $k(\sqrt{-d})$
Eine Bemerkung über kubische Einheiten
The genus fields of algebraic number fields
On 2-adic L-functions and cyclotomic invariants
Integral bases for bicyclic biquadratic fields over quadratic subfields
Remarks on the class number of an imaginary bicyclic biquadratic number field
Class number formulae for bicubic fields
Rational compositum genus for a pure cubic field
Relations between $K_2$ and Galois cohomology
On the conjecture of Birch and Swinnerton-Dyer
On a conjecture of Brandler
Konvexe Untergruppen in algebraischen Zahlkörpern
Fields with large Kronecker constants
Lower bounds for discriminants of number fields. II
Ein Endlichkeitssatz der Galois-Kohomologie
On Artin's conjecture and Euclid's algorithm in global fields
The calculation of $L_p(1,\chi)$
On the degree of the splitting field of an irreducible binomial
Arithmetische Ausdeutung der Klassenzahlformel für einfach reelle kubische Zahlkörper
Regulatorabschätzungen für total reelle algebraische Zahlkörper
Sur le nombre de classes de certaines extensions, metacycliques sur $\mathbb{Q}$ ou sur un corps quadratiques imaginaire
On Grunwald-Hasse-Wang's theorem
On some truncated units in algebraic number fields of degree $n> 3$
On the values of Hecke's $L$-functions at non-positive integers
Stickelberger ideals
Norm maps for formal groups. IV
Computing the number of totally positive circular units which are squares
On a theorem of Delaunay and some related results
Tours de corps de classes et estimations de discriminants
Einige Bemerkungen zu Einheiten in reinen kubischen Körpern
``Verstümmelte Grundeinheiten für biquadratische und bikubische Zahlkörper
A generalization of Berwick's unit algorithm
Zur Theorie der Ringklassenkörper über imaginär-quadratischen Zahlkörpern
Icosahedral Galois representations
Zeta functions and integral representation theory
Über eine Erweiterung der Wittschen Reduktion bei der Bestimmung der Schurindizes von endlichen Gruppen über lokalen Körpern
Classification of the primitive representations of the Galois group of local fields
Schur indices over the 2-adic field
A class of periodic Jacobi-Perron algorithms in pure algebraic number fields of degree $n\geq 3$
Higher explicit reciprocity laws
Some lattices over $Q(\sqrt{-3})^*$
Arithmétique d'une extension galoisienne à groupe d'inertie cyclique
On the self-duality of a ring of integers as a Galois module
Units in totally complex $S_3$ fields
Galois groups of intersections of local fields
On the local Langlands conjecture for GL(2)
Atomare Kronecker-Klassen mit speziellen Galoisgruppen
Décomposition du Galois-module des entiers d'une extension cyclique de degré premier d'un corps de nombres ou d'un corps local
Die Relationen von Gaußschen Summen und Kreiseinheiten
The class number of $\mathbb Q(\sqrt{-p})$ modulo 4, for $p\equiv 3$ (mod 4) a prime
Iwasawa invariants and Kummer congruences
Classes and units of real cyclic extensions of degree 4 of $\mathbb{Q}$
Unités cyclotomiques, unités semi-locales et $\mathbb{Z}_\ell$-extensions
On the units of a non-abelian Galois extension of degree $pq$ of the rational field, $p$ and $q$ odd prime numbers
An explicit formula for the fundamental units of a real pure sextic number field and its Galois closure
Units and class numbers of a dihedral Galois extension of $\mathbb{Q}$
Small discriminants
Sur la structure galoisienne du groupe des unités d'un corps abélien de type $(p,p)$
On the $p$-rank of the class group of a composite of algebraic number fields.
On the equation $\zeta_K(s)=\zeta_{K'}(s)$
An arithmetical application of elliptic functions to the theory of cubic residues
Sur la divisibilite par 8 et 16 des nombres de classes d'ideaux des corps quadratiques $Q(\sqrt{2p})$ et $Q(\sqrt{-2p})$
Frobenius Galois groups over quadratic fields
On the first factor of the class number of prime cyclotomic fields
Kronecker classes of algebraic number fields
On certain ray class invariants of real quadratic fields
Arithmetic properties of the idéle discriminant
$\mathfrak p$-adic fields having the same type of algebraic extensions
Die Galois-Theorie
An algorithm for Halter-Koch units
A classical invitation of algebraic numbers and class fields. With two appendices by Olga Taussky: ``Artin's 1932 Göttingen lectures on class field theory and ``Connections between algebraic number theory and integral matrices.
Note on dyadotropic cubics
On the Stickelberger ideal and the circular units of a cyclotomic field
Verallgemeinerung eines Satzes von Rabinowitsch über imaginär-quadratische Zahlkörper.
Discriminants of certain algebraic number fields.
The genus theory of number fields
On the Order and Degree of Solutions to Pure Equations
Computations on the growth of the first factor for prime cyclotomic fields
The analytic theory of algebraic numbers
Relative Integral Bases
Some remarks on L-functions and class numbers
On 3-class groups of pure cubic fields.
On the Iwasawa Invariants of Totally Real Number Fields
On normal radical extensions of the rationals
Class number formulae for imaginary quadratic fields.
On the integral basis of the maximal real subfield of a cyclotomic field.
An integral basis of the algebraic number field Q().
Einige Klassen von endlichen GALOIS-Moduln mit HASSE-Prinzip
On Fermat's last theorem.
Comparaison des $2$-groupes des classes d'idéaux au sens large et au sens étroit d'un corps quadratique réel
Sur le 2-groupe des classes d'idéaux des corps quadratiques.
Note on class number factors and prime decompositions
On nilpotent factors of congruent ideal class groups of Galois extensions
Kuroda's class number relation
The Pythagorean closure of fields.
A Proof of the Normal Basis Theorem
On the Galois groups of cubics and trinomials
On an Algorithm of Billevich for Finding Units in Algebraic Number Fields
Consecutive integers in algebraic number fields.
Note on the class-number of the maximal real subfield of a cyclomatic field.
Zur Existenz einfacher abelscher Varietäten mit komplexer Multiplikation.
Explizite Darstellungen von Einheiten und ihre Anwendung auf Mehrklassigkeitsfragen bei reell-quadratischen Zahlkörpern. II.
Extensions of the Hasse norm theorem
The Hasse norm principle for Abelian extensions of number fields
Euclid's Algorithm in the Cyclotomic Field Q(ζ 16 )
A criterion for the class number of a pure quintic field to be divisible by 5.
Gaining Units from Units
Relation entre les 2-groupes des classes d'idéaux au sens ordinaire et restreint de certains corps de nombres
On l ‐class groups of certain number fields
Dyadotropic Polynomials
Integrality Properties of the Values of Partial Zeta Functions
Units with norm - 1 and signatures of units.
Elliptic Curves and Class Groups of Quadratic Fields
Computations on the growth of the first factor for prime cyclotomic fields II
Certain Pure Cubic Fields With Class-Number One
Dihedral Field Extensions of Order 2p Whose Class Numbers are Multiples of p
Die Klassenzahl der Teilkörper abelscher Erweiterungen imaginär-quadratischer Zahlkörper. I.
Die Klassenzahl der Teilkörper abelscher Erweiterungen imaginär-quadratischer Zahlkörper. II.
Ideal-theoretic characterization of the relative genus field.
On Kronecker Classes of Atomic Extensions
Über den 3-Rang von quadratischen Zahlkörpern und den Rang gewisser elliptischer Kurven
Unités de norme -1 de Q (√p) et corps de classes de degré 8 de Q (√-p) où p est un nombre premier congru à 1 modulo 8
A Nonsymmetric Hasse-Minkowski Theorem
Norms of Normal Integral Generators
Minorations de discriminants [d’après A. M. Odlyzko]
Interpretation of the p-Adic Log Gamma Function and Euler Constants Using the Bernoulli Measure
Artin Root Numbers for Real Characters
On the central class field mod of Galois extensions of an algebraic number field
A remark concerning the 2-adic number field
A rational sixteenth power reciprocity law
A counterexample for the local analogy of a theorem by lwasawa and Uchida
The class number of pure fields of prime degree
The class number of pure fields of prime degree
Proper solutions of the imbedding problem with restricted ramification
Integrality of Galois Jacobi Sums
Groupes d'unités elliptiques
Polynomials with galois group psl(2,7)
SL(2,5) and Frobenius Galois Groups Over Q
Real characters of the ideal class-group and the narrow ideal class-group of Q(√d)
Weil-Darstellungen und lokale Galoistheorie
Ergänzungen zu Weils Exercises dyadiques
A Note on Class-Number One in Pure Cubic Field
FORMAL GROUPS AND THE NORM RESIDUE SYMBOL
THE $ \mathfrak{p}$-ADIC ZETA-FUNCTION OF AN IMAGINARY QUADRATIC FIELD AND THE LEOPOLDT REGULATOR
On the module structure of a p-extension over a -adic number field
ON RAMIFICATION OF p-EXTENSIONS OF $p$-ADIC NUMBER FIELDS
On explicit reciprocity laws. II.
Invarianten des total reellen Körpers siebten Grades mit Minimaldiskriminante
Some unramified abelian extensions of algebraic number fields.
Genera in Abelian Extensions
Plongement d'une extension d'ordre p ou p2 dans une surextension non abelienne d'ordre p3.
On Euclidean rings of integers in cyclotomic fields.
On 2-rank of the ideal class groups of algebraic number fields.
Über das Einbettungsproblem für globale Körper bei beschränkter Verzweigung
Irregular Primes and Cyclotomic Invariants
Reduction theory in algebraic number fields
A remark of a Neukirch's conjecture
Über eine Klasse von L-Funktionen algebraischer Zahlkörper
On certain algebraic groups attached to local number-fields.
On the fundamental units of real quadratic fields
Zur Idealstruktur in Nichtstandardmodellen von Dedekindringen.
On relative class numbers of certain quadratic extensions
The Simplest Cubic Fields
Units and discriminants of algebraic number fields
Modules sur certains anneaux de Dedekind.
Eine p-adische Theorie der Zetawerte. II.
Steinitz Classes of Cyclic Extensions of Degree l r
Pure quartic number fields whose class numbers are even.
The Distribution of Ideal Class Numbers of Real Quadratic Fields
The 3‐class groups of non‐Galois cubic fields—I
The 3‐class groups of non‐Galois cubic fields–II
Critère de parité du nombre de classes des extensions abéliennes réelles de $Q$ de degré impair
Unit signatures, and even class numbers, and relative class numbers.
On the class-number of the maximal real subfield of a cyclotomic field.
ON CERTAIN VALUES OF p-ADIC L-FUNCTIONS
VANDIVER'S CONGRUENCE FOR THE RELATIVE CLASS NUMBER OF AN IMAGINARY ABELIAN FIELD
On the norms of algebraic integers
On the cyclotomic invariants of Iwasawa.
Some Applications of ABHYANKAR's Lemma
ON BIQUADRATIC FIELDS
A Note on l-Class Groups of Number Fields
Berechnung kleiner Diskriminanten total reeller algebraischer Zahlkörper.
Class number relations in pure sextic fields.
On p-adic L-functions and cyclotomic fields
Locally free modules over arithmetic orders.
On the module structure of the ring of all integers of a p-adic number field
Central class numbers in central class field towers
Galois module structure of classgroups and units
A purely algebraic proof of special cases of Tchebotarev's theorem
On Complex Quadratic Fields with Class-Number Two
Computation of the Ideal Class Group of Certain Complex Quartic Fields. II
Periodic expansions and units in quadratic and cubic number fields.
Units and Periodic Jacobi-Perron Algorithms in Real Algebraic Number Fields of Degree 3
Artin Root Numbers, Conductors, and Representations for Generalized Quaternion Groups
Resolvents and trace form
On the Iwasawa invariants of imaginary abelian fields
Läuchli's algebraic closure of Q
A Computational Technique for Determining the Class Number of a Pure Cubic Field
On the norm form of a finite Galois extension over 𝑄
Module Conductors and Module Resolvents
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Primes which remain irreducible in a normal field
Completeness of the absolute Galois group of the rational number field
Berechnung von Einheiten nach Lagrange.
Zahlkörper mit gleicher Primzerlegung.
Class number formulae for imaginary quadratic fields. II.
On the Hasse norm principle.
A note on Friedlander's paper "On the class numbers of certain quadratic extensions"
On Sums of Three Integral Squares in Algebraic Number Fields
Onp-adicL-functions and cyclotomic fields. II
A note on Hilbert class fields of algebraic number fields
An Effective Number Geometric Method of Computing the Fundamental Units of an Algebraic Number Field
ON THE CLASS FIELD TOWER OF AN IMAGINARY QUADRATIC NUMBER FIELD
On class numbers of some cyclotomic fields.
Signatures of units and congruences (mod 4) in certain real quadratic fields.
Hilbert’s twelfth problem and 𝐿-series
On certain ray class invariants of real quadratic fields
Structure of l ‐class groups of certain number fields and ℤ _l ‐extensions
Table of the cyclotomic class numbers ℎ*(𝑝) and their factors for 200<𝑝<521
The p-Adic Log Gamma Function and p-Adic Euler Constants
Die Struktur der Einheitengruppe für eine Klasse metazyklischer Erweiterungen algebraischer Zahlkörper.
Einheiten in algebraischen Funktionen- und Zahlkörpern.
The Hasse norm principle in cyclotomic number fields.
The Hasse norm principle in non-abelian extensions.
Galois module structure of integers of relative abelian extensions.
On Some Families of Imaginary Quadratic Fields
Computation of the 2-Rank of Pure Cubic Fields
On K 2 and Z l Extensions of Number Fields
Determining the Fundamental Unit of a Pure Cubic Field Given Any Unit
Some Problems of Galois Module Structure for Wild Extensions
A Probable Hasse Principle for Pencils of Quadrics
On the central ideal class group of cyclotomic fields
On Galois groups of class two extensions over the rational number field
A note on formal groups and zeta functions.
Die Einseinheitengruppe von p-Erweiterungen regulärer -adischer Zahlkörper als Galoismodul.
Invariants of the trace-form of a number field
Divisibility of class numbers of real cyclic extensions of degree 4 over Q.
The Ideal Class Groups of Two Cyclotomic Fields
Die p-Vervollständigung der multiplikativen Gruppe einer p-Erweiterung eines irregulären p-adischen Zahlkörpers.
Class numbers of binary quadratic forms over algebraic number fields.
On Dirichlet's Class Number Formula
The Euclidean Condition in Pure Cubic and Complex Quartic Fields
On the maximal abelianℓ-extension of a finite algebraic number field with given ramification
Calculation of the Regulator of Q(√D) by use of the Nearest Integer Continued Fraction Algorithm
Dyadotropic Polynomials. II
Intersections of Conjugate Fields of Finite Corank over Hilbertian Fields
On the module structure in a cyclic extension over a -adic number field
The Hasse Norm Theorem for Non-Cyclic Extensions of the Rationals
Fields generated by linear combinations of roots of unity, II.
The ambiguous class group and the genius group of certain non‐normal extensions
A Note on K 2 and the Theory of ℤ p -Extensions
Galois Module Structure of Rings of Integers in Kummer Extensions
Zur Parametisierung reell-quadratischer Zahlkörper.
Über die Grundeinheit der reell-quadratischen Zahlkörper Q( A2N2 + BN + C).
On congruence topologies in number fields.
Independent systems of units in certain algebraic number fields.
Modular units inside cyclotomic units
Nombres de Hurwitz et unités elliptiques. Un critère de régularité pour les extensions abéliennes d'un corps quadratique imaginaire
Quadratic Fields With 3-Rank Equal to 4
Norm distribution in Galois orbits.
On Computing Artin L-Functions in the Critical Strip
The universal ordinary distribution
The Z/2 Z cohomology of the universal ordinary distribution
On explicit reciprocity laws.
On the radius of convergence of the p-adic L-function
Diophantine Properties of Subfields of ~ Q  
On the 3-Rank of Quadratic Fields and the Euler Product
Number Fields with Prescribed l-Class Groups
Notes on étale cohomology of number fields
Zum Hauptidealsatz von Tannaka‐Terada
Die Einseinheitengruppen höherer Stufen einer zerfallenden zahm‒verzweigten Erweiterung als G<scp>ALOIS</scp>moduln
Zur GALOISschen Theorie der maximalenp-Erweiterungen mit vorgegebenen Verzweigungsstellen
Steinitz Classes in Quartic Fields
Eine Bemerkung zum Existenzsatz von Grunwald-Hasse-Wang.
Lower bounds for discriminants of number fields
Über die Einheitengruppe der reinen algebraischen Zahlkörper sechsten Grades.
On the quartic character of quadratic units.
Lectures on P-Adic L-Functions. (AM-74)
Profinite Groups, Arithmetic, and Geometry. (AM-67)
Normal integral bases and the Galois groups of Galois extensions of number fields.
What is a Reciprocity Law?
Über die 2‐Komponente der Klassengruppe quadratischer Zahlkörper mit zwei Diskriminantenteilern
Examples of Iwasawa invariants
Class Numbers and μ-Invariants of Cyclotomic Fields
Symmetric matrices, characteristic polynomials, and Hilbert symbols over local number fields
On discriminants and maximal orders
Einbettungsprobleme mit lokaler Vorgabe und freie Produkte lokaler Galoisgruppen.
Examples of Iwasawa invariants, II
Über die Anzahl der Erweiterungen eines algebraischen Zahlkörpers mit einer gegebenen abelschen Gruppe als Galoisgruppe
On the embedding problem for nonsolvable Galois groups of algebraic number fields: Reduction theorems
Galois module structure of rings of integers
On the divisibility of the class number of imaginary quadratic fields
Some analytic estimates of class numbers and discriminants
A normal integral basis theorem
Units of irregular cyclotomic fields
Annulation du groupe des $\ell$-classes généralisées d'une extension abélienne réelle de degré premier à $\ell$
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