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Second order strong divisibility sequences in an algebraic number field

Andrzej Schinzel (1987)

Archivum Mathematicum

Selberg Formulae for Gaussian integers

Graeme Cohen (1975)

Acta Arithmetica

Semigroup crossed products and Hecke algebras arising from number fields.

Arledge, Jane, Laca, Marcelo, Raeburn, Iain (1997)

Documenta Mathematica

Sequences of algebraic integers and density modulo $1$

Roman Urban (2007)

Journal de Théorie des Nombres de Bordeaux

We prove density modulo $1$ of the sets of the form ${μ^{m} λ^{n} ξ + r_{m} : n, m \in ℕ},$ where $λ, μ \in ℝ$ is a pair of rationally independent algebraic integers of degree $d \geq 2,$ satisfying some additional assumptions, $ξ \neq 0,$ and $r_{m}$ is any sequence of real numbers.

Solution des problèmes de Favard

M. LANGEVIN (1986/1987)

Seminaire de Théorie des Nombres de Bordeaux

Solution des problèmes de Favard

Michel Langevin (1988)

Annales de l'institut Fourier

Pour tout $c < 2$ , on calcule un rang $D (c)$ tel que tout entier algébrique $x$ de degré au moins $D (c)$ ait deux conjugués $x^{'}, x^{''}$ vérifiant $| x^{'} - x^{''} | \geq c$ . De plus, on donne une nouvelle preuve de l’égalité $D (\sqrt{3}) = 2$ .

Some families of finite groups and their rings of invariants

Stefan Kühnlein (1999)

Acta Arithmetica

Some remarks about the power residue symbol

(1994)

Acta Arithmetica

Steinitz classes of a nonabelian extension of degree $p^{3}$

James Carter (1996)

Colloquium Mathematicae

Steinitz classes of nonabelian extensions of degree p³

James E. Carter (1997)

Acta Arithmetica

Steinitz classes of some abelian and nonabelian extensions of even degree

Alessandro Cobbe (2010)

Journal de Théorie des Nombres de Bordeaux

The Steinitz class of a number field extension $K / k$ is an ideal class in the ring of integers $𝒪_{k}$ of $k$ , which, together with the degree $[K : k]$ of the extension determines the $𝒪_{k}$ -module structure of $𝒪_{K}$ . We denote by $R_{t} (k, G)$ the set of classes which are Steinitz classes of a tamely ramified $G$ -extension of $k$ . We will say that those classes are realizable for the group $G$ ; it is conjectured that the set of realizable classes is always a group.In this paper we will develop some of the ideas contained in [7] to obtain some...

Steinitz classes of tamely ramified nonabelian extensions of odd prime power order

Alessandro Cobbe (2011)

Acta Arithmetica

Structure galoisienne relative des anneaux d' entiers

B. SODAIGUI (1986/1987)

Seminaire de Théorie des Nombres de Bordeaux

Structure of group invariants of a quasiperiodic flow.

Bakker, Lennard F. (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Sums of roots of unity.

Timo Ojala (1975)

Mathematica Scandinavica

Sur des hauteurs alternatives. I.

P. Philippon (1991)

Mathematische Annalen

Sur l’anneau des entiers des extensions galoisiennes non abéliennes de degré $p q$ des rationnels

Jean Cougnard (1974)

Mémoires de la Société Mathématique de France

Sur le groupe des unités de corps de nombres de degré $2$ et $4$

M’hammed Ziane (2007)

Journal de Théorie des Nombres de Bordeaux

Nous déterminons sous certaines hypothèses, un système fondamental d’unités du corps non pur $K = ℚ (ω)$ et de son sous-corps quadratique, où $ω$ est solution du polynôme $f (X) = X^{4} + d^{- 2} M_{6} X^{2} - M_{4},$ avec $M_{6} = D^{6} + 6 D^{4} d + 9 D^{2} d^{2} + 2 d^{3}$ , $M_{4} = D^{4} + 4 D^{2} d + 2 d^{2}$ , $d | D$ , $d$ , $D \in ℕ$ , non nuls.

Sur le théorème des idéaux premiers

C. Touibi, H. Smida Zargouni (1989)

Colloquium Mathematicae

Sur les polynômes à coefficients entiérs et de discriminant donné

Kalman Győry (1973)

Acta Arithmetica

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