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Eigenspaces of the ideal class group

Cornelius Greither, Radan Kučera (2014)

Annales de l’institut Fourier

The aim of this paper is to prove an analog of Gras’ conjecture for an abelian field $F$ and an odd prime $p$ dividing the degree $[F : ℚ]$ assuming that the $p$ -part of $Gal (F / ℚ)$ group is cyclic.

Ein Satz über relativ-Galoissche Zahlkörper und seine Anwendang auf relativ-Abelsche Zahlkörper

H. Hasse (1930)

Mathematische Zeitschrift

Eine Klassenzahlformel für singuläre Moduln der Picardschen Modulgruppen

Jan Feustel (1990)

Compositio Mathematica

Ensembles de nombres algébriques et transformations rationnelles

Gérard Rauzy (1971)

Mémoires de la Société Mathématique de France

Enumerating quartic dihedral extensions of $ℚ$ with signatures

Henri Cohen (2003)

Annales de l’institut Fourier

In a previous paper, we have given asymptotic formulas for the number of isomorphism classes of $D_{4}$ -extensions with discriminant up to a given bound, both when the signature of the extensions is or is not specified. We have also given very efficient exact formulas for this number when the signature is not specified. The aim of this paper is to give such exact formulas when the signature is specified. The problem is complicated by the fact that the ray class characters which appear are not all genus characters....

Errata to the papers : “Connections between $B_{2, χ}$ for even quadratic Dirichlet characters $χ$ ” and “Class numbers of appropriate imaginary quadratic fields, parts I and II”

Jerzy Urbanowicz (1991)

Compositio Mathematica

Erratum “On the computation of quadratic $2$ -class groups”

W. Bosma, P. Stevenhagen (1997)

Journal de théorie des nombres de Bordeaux

Erratum to "Cohomology sets inside arithmetic groups" (Acta Arith. 107 (2003), 27-33)

Stefan Kühnlein (2003)

Acta Arithmetica

Estimates of regulators and class numbers in function fields.

H.-G. Quebbemann (1991)

Journal für die reine und angewandte Mathematik

Étude d'un idéal particulier, d'indice fini dans le carré de l'idéal d'augmentation, associé à un caractère de Dirichlet d'un groupe fini

Hassan Oukhaba, Gilles Robert (1991)

Journal de théorie des nombres de Bordeaux

We describe here two sets of generators of an ideal $Δ (ψ) = M (ψ)$ , of finite index inside the square $I^{2}$ of the augmentation ideal $I$ of $ℤ [G]$ , associated to the Dirichlet character $ψ$ of the finite group $G$ . That peculiar ideal first appeared in questions related to the computation of class number formulas for abelian non ramified extensions of $𝒜$ -fields cf. [2] and [3], satisfying certain special conditions which are outlined in the introduction of [1]. A rough idea of these formulas is given in §§2 and 6.

Examples of ...-invariants.

Nancy Childress (1990)

Manuscripta mathematica

Explicit upper bounds for |L(1,χ)| for primitive even Dirichlet characters

Stéphane Louboutin (2002)

Acta Arithmetica

Explicit upper bounds for the average order of $d_{n} (m)$ and application to class number.

Bordellès, Olivier (2002)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Exponent of class group of certain imaginary quadratic fields

Kalyan Chakraborty, Azizul Hoque (2020)

Czechoslovak Mathematical Journal

Let $n > 1$ be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $ℚ (\sqrt{x^{2} - 2 y^{n}})$ whose ideal class group has an element of order $n$ . This family gives a counterexample to a conjecture by H. Wada (1970) on the structure of ideal class groups.

Exponents of the class groups of complex quadratic fields

P. Weinberger (1973)

Acta Arithmetica

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