Über Den Bizyklischen Biquadratischen Zahlkörper

DOI10.1017/S0027763000000088zbMath0074.03001OpenAlexW1568579026MaRDI QIDQ3238382

Publication date: 1956

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0027763000000088

zbMATH Keywords

Function Fields Number Fields

Related Items (63)

On the trace formula of the Hecke operators and the special values of the second L-functions attached to the Hilbert modular forms ⋮ Sur une question de capitulation ⋮ On the units of cubic and bicubic fields ⋮ Monogenic biquadratic fields ⋮ Stark's conjecture and Abelian $L$-functions with higher order zeros at $s=0$ ⋮ A multiquadratic field generalization of Artin's conjecture ⋮ Abelian varieties with several principal polarizations ⋮ Reelle biquadratische Zahlkörper mit ungerader Klassenzahl. (Real biquadratic number fields with odd class number) ⋮ Imaginary quadratic fields $k$ with cyclic $\text{Cl}_2(k^1)$ ⋮ Classification of metabelian 2-groups $G$ with $\mathbf{G}^{\mathrm{ab}} (\mathbf{2},\mathbf{2}^{\mathbf n})$, $\mathbf n\geq \mathbf 2$, and rank $\mathbf d(\mathbf G^{\prime})=\mathbf 2$. Applications to real quadratic number fields ⋮ Quartic fields with large class numbers ⋮ Capitulation in unramified quadratic extensions of real quadratic number fields ⋮ Sur les $\ell$-classes d'idéaux dans les extensions cycliques rélatives de degré premier $\ell$. I ⋮ The fundamental unit in quadratic extensions of imaginary quadratic fields ⋮ Structure of 2-class groups in the $\mathbb{Z}_2$-extensions of certain real quadratic fields ⋮ On the class groups of dihedral groups ⋮ The unit group of some fields of the form $\mathbb{Q}(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-l})$ ⋮ $\Gamma $-extensions et invariants cyclotomiques ⋮ Unit signature ranks in real biquadratic and multiquadratic number fields ⋮ Remarks on unit indices of imaginary abelian number fields. II ⋮ Unit indices of imaginary abelian number fields of type $(2,2,2)$ ⋮ A note on a paper of Iwasawa ⋮ Galois extensions of prime degree ⋮ Some real quadratic number fields whose Hilbert 2-class fields have class number congruent to 2 modulo 4 ⋮ On the maximal unramified pro-2-extension of $\mathbb Z_2$-extensions of certain real quadratic fields. ⋮ Sur le rang du 2-groupe de classes de 𝑄({√{𝑚}},{√{𝑑}}) où 𝑚=2 ou un premier 𝑝≡1(𝑚𝑜𝑑4) ⋮ The non-normal quartic CM-fields and the octic dihedral CM-fields with relative class number two ⋮ On the second Hilbert 2-class field of real quadratic number fields with 2-class group isomorphic to $(2,2^n)$, $n\geq 2$ ⋮ The narrow 2-class field tower of some real quadratic number fields ⋮ On the unit index of some real biquadratic number fields ⋮ The Iwasawa invariant $\mu$ vanishes for $\mathbb{Z}_2$-extensions of certain real biquadratic fields ⋮ Imaginary multiquadratic fields of class number 1 ⋮ Computing associated orders and Galois generating elements of unit lattices ⋮ Capitulation in the absolutely abelian extensions of some number fields. II ⋮ The unit signature rank deficiency is unbounded over cyclotomic fields ⋮ ON THE STRONGLY AMBIGUOUS CLASSES OF 𝕜/ℚ(i) WHERE $\mathds{k} = {\mathbb Q}(\sqrt{2p_{1}p_{2}, i})$ ⋮ Short Generators Without Quantum Computers: The Case of Multiquadratics ⋮ Hasse Unit Indices of Dihedral Octic CM-Fields ⋮ On a theorem of Kawamoto on normal bases of rings of integers ⋮ The imaginary abelian number fields with class numbers equal to their genus class numbers ⋮ LE 2-RANG DU GROUPE DE CLASSES DE CERTAINS CORPS BIQUADRATIQUES ET APPLICATIONS ⋮ On the Iwasawa $\lambda $-invariant of the cyclotomic $\mathbb {Z}_2$-extension of $\mathbb {Q}(\sqrt {p} )$ ⋮ Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group ⋮ Sur la structure galoisienne du groupe des unités d'un corps abélien de type $(p,p)$ ⋮ On the Ideal Class Group of Real Biquadratic Fields ⋮ Geometry of biquadratic and cyclic cubic log-unit lattices ⋮ Hasse's class number product formula for generalized Dirichlet fields and other types of number fields ⋮ On the parity of the class number of multiquadratic number fields ⋮ The group Gal(k3(2)|k) for k = ℚ(−3,d) of type (3,3) ⋮ Real quadratic fields with abelian 2-class field tower ⋮ Kuroda's formula and arithmetic statistics ⋮ Ein Satz über die Geschlechter relativ-zyklischer Zahlkörper von Primzahlgrad und seine Anwendung auf biquadratisch-bizyklische Körper ⋮ On the 2-class group of $\mathbb{Q}(\sqrt{d},i)$ ⋮ Sur quelques questions dans la théorie des corps biquadratiques ⋮ Sur les $\ell$-classes d'idéaux dans les extensions cycliques rélatives de degré premier $\ell$. II ⋮ Refined lower bounds on the 2-class number of the Hilbert 2-class field of imaginary quadratic number fields with elementary 2-class group of rank 3 ⋮ Class numbers of imaginary abelian number fields ⋮ Einheitenbasen für parametrisierte Zahlkörper vierten und achten Grades mit beliebigem reell-quadratischen Teilkörper ⋮ Tame pro-2 Galois groups and the basic ℤ₂-extension ⋮ On Farrell-Tate cohomology of $\operatorname{GL}_3$ over rings of quadratic integers ⋮ A note on $\ell$-class groups of certain algebraic number fields ⋮ Norm form equations and linear divisibility sequences ⋮ Bases normales d'entiers relatives quadratiques. (Normal relative quadratic integral bases)

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