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Damey et Payan ont montré que la différence des 4-rangs des groupes des classes d’idéaux des corps quadratiques $Q (\sqrt{a})$ et $Q (\sqrt{- a})$ est majorée par ( $a$ étant positif) : $0 \leq {dim}_{4} H_{Q (\sqrt{- a})} - {dim}_{4} H_{Q (\sqrt{a})} \leq 1 .$ Dans ce papier, l’auteur généralise cette propriété en remplaçant le corps de base $Q$ par un corps de nombres $k$ quelconque. La méthode employée est issue du “Spiegelungssatz” de Leopoldt.

Relations monomiales entre périodes p-adiques.

Roland Gillard (1988)

Inventiones mathematicae

Relations qui existent entre les formes quadratiques de deux déterminants $D$ et $D e^{2}$ (Disquisitiones, n° 213 et 214)

P. Pépin (1905)

Journal de Mathématiques Pures et Appliquées

Relative block semigroups and their arithmetical applications

Franz Halter-Koch (1992)

Commentationes Mathematicae Universitatis Carolinae

We introduce relative block semigroups as an appropriate tool for the study of certain phenomena of non-unique factorizations in residue classes. Thereby the main interest lies in rings of integers of algebraic number fields, where certain asymptotic results are obtained.

Relative Bogomolov extensions

Robert Grizzard (2015)

Acta Arithmetica

A subfield K ⊆ ℚ̅ has the Bogomolov property if there exists a positive ε such that no non-torsion point of $K^{\times}$ has absolute logarithmic height below ε. We define a relative extension L/K to be Bogomolov if this holds for points of $L^{\times} ∖ K^{\times}$ . We construct various examples of extensions which are and are not Bogomolov. We prove a ramification criterion for this property, and use it to show that such extensions can always be constructed if some rational prime has bounded ramification index in K.

Relative Brauer Groups. I.

B. Fein, M. Schacher (1981)

Journal für die reine und angewandte Mathematik

Relative Brauer groups. III.

Murray Schacher, Burton Fein (1982)

Journal für die reine und angewandte Mathematik

Relative Galois module structure of integers of abelian fields

Nigel P. Byott, Günter Lettl (1996)

Journal de théorie des nombres de Bordeaux

Let $L / K$ be an extension of algebraic number fields, where $L$ is abelian over $ℚ$ . In this paper we give an explicit description of the associated order $𝒜_{L / K}$ of this extension when $K$ is a cyclotomic field, and prove that $o_{L}$ , the ring of integers of $L$ , is then isomorphic to $𝒜_{L / K}$ . This generalizes previous results of Leopoldt, Chan Lim and Bley. Furthermore we show that $𝒜_{L / K}$ is the maximal order if $L / K$ is a cyclic and totally wildly ramified extension which is linearly disjoint to $ℚ^{(m^{'})} / K$ , where $m^{'}$ is the conductor of $K$ .

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Displaying 261 – 280 of 547

Relations de dépendance linéaire entre des logarithmes de nombres algébriques

Relations de distributions et exemples classiques

Relations de récurrence modulo m

Relations d'inégalités effectives en théorie algébrique des nombres

Relations diophantiennes et la solution négative du 10e problème de Hilbert

Relations entre les 2-groupes de classes d’idéaux des extensions quadratiques $k (\sqrt{d})$ et $k (\sqrt{- d})$

Relations monomiales entre périodes p-adiques.

Relations qui existent entre les formes quadratiques de deux déterminants $D$ et $D e^{2}$ (Disquisitiones, n° 213 et 214)

Relative block semigroups and their arithmetical applications

Relative Bogomolov extensions

Relative Brauer Groups. I.

Relative Brauer groups. III.

Relative Galois module structure of integers of abelian fields

Relative Galois module structure of integers of local abelian fields

Relative Galois module structure of rings of integers of cyclomatic fields.

Relative Gleichverteilung in lokalkompakten Räumen II.

Relative integral basis for algebraic number fields.

Relative Kloosterman integrals for GL(3)

Relative Lubin-Tate Formal Groups and Galois module structure.

Relative modular symbols and p-adique Rankin-Selberg convolutions.

Currently displaying 261 – 280 of 547