A generalization of Voronoï’s Theorem to algebraic lattices

Okuda, Kenji; Yano, Syouji

doi:10.5802/jtnb.742

Okuda, Kenji ; Yano, Syouji ¹

¹ Department of Mathematics, Graduate School of Science, Osaka-University, 1-1 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Journal de théorie des nombres de Bordeaux, Tome 22 (2010) no. 3, pp. 727-740.

Résumé
Abstract

Soient $K$ un corps de nombres et $𝒪_{K}$ l’anneau des entiers de $K$ . Dans cet article, nous prouvons un analogue du théorème de Voronoï pour les $𝒪_{K}$ -réseaux, et la finitude du nombre de classes de $𝒪_{K}$ -réseaux parfaits, à similitude près.

Let $K$ be an algebraic number field and $𝒪_{K}$ the ring of integers of $K$ . In this paper, we prove an analogue of Voronoï’s theorem for $𝒪_{K}$ -lattices and the finiteness of the number of similar isometry classes of perfect $𝒪_{K}$ -lattices.

MR Zbl | 1 citation dans Numdam

DOI : 10.5802/jtnb.742

Affiliations des auteurs :

Okuda, Kenji ; Yano, Syouji ¹

¹ Department of Mathematics, Graduate School of Science, Osaka-University, 1-1 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

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     title = {A generalization of {Vorono{\"\i}{\textquoteright}s} {Theorem} to algebraic lattices},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
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     publisher = {Universit\'e Bordeaux 1},
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Okuda, Kenji; Yano, Syouji. A generalization of Voronoï’s Theorem to algebraic lattices. Journal de théorie des nombres de Bordeaux, Tome 22 (2010) no. 3, pp. 727-740. doi : 10.5802/jtnb.742. http://www.numdam.org/articles/10.5802/jtnb.742/

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