scientific article

zbMath0885.11001MaRDI QIDQ2785516

Helmut Koch

Publication date: 24 February 1997

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

ordersquadratic fieldscontinued fractionsclass number formulasramification groupscyclotomic fieldsvaluation theoryRiemann-Roch theoremclass field theorygeometry of numbersalgebraic numberselementary number theoryinertia groupalgebraic function fieldGaussian sumsprime number theoryadelesideal theoryGrössencharactersDirichlet's unit theoremTate's thesisidelespublic key cryptologydecomposition groupfinite normal extensionsfunctional equation for Hecke \(L\)-series

Mathematics Subject Classification ID

Quadratic extensions (11R11) Units and factorization (11R27) Class field theory (11R37) Continued fractions (11A55) Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42) Distribution of prime ideals (11R44) Algebraic numbers; rings of algebraic integers (11R04) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory (11-01) Algebraic number theory: global fields (11Rxx) Elementary number theory (11Axx)

Related Items (10)

On the ring of \(p\)-integers of a cyclic \(p\)-extension over a number field ⋮ Counting nilpotent Galois extensions ⋮ On the representation of integers as linear combinations of consecutive values of a polynomial ⋮ What You Should Know About Integer-Valued Polynomials ⋮ Remarks on profinite groups having few open subgroups ⋮ The special case of cyclotomic fields in quantum algorithms for unit groups ⋮ On the set of integral solutions of the pell equation in global function fields ⋮ ON m-COVERS AND m-SYSTEMS ⋮ The relative theorem of Schanuel ⋮ Root lattices in number fields

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