A generalization of Voronoï’s Theorem to algebraic lattices
Kenji Okuda; Syouji Yano1
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, Volume 22 (2010) no. 3, pp. 727-740.

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.

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.

DOI: 10.5802/jtnb.742

Kenji Okuda ; Syouji Yano 1

1 Department of Mathematics, Graduate School of Science, Osaka-University, 1-1 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan 
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Kenji Okuda; Syouji Yano. A generalization of Voronoï’s Theorem to algebraic lattices. Journal de théorie des nombres de Bordeaux, Volume 22 (2010) no. 3, pp. 727-740. doi : 10.5802/jtnb.742. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.742/

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