Let be an algebraic number field and the ring of integers of . In this paper, we prove an analogue of Voronoï’s theorem for -lattices and the finiteness of the number of similar isometry classes of perfect -lattices.
Soient un corps de nombres et l’anneau des entiers de . Dans cet article, nous prouvons un analogue du théorème de Voronoï pour les -réseaux, et la finitude du nombre de classes de -réseaux parfaits, à similitude près.
@article{JTNB_2010__22_3_727_0, author = {Okuda, Kenji and Yano, Syouji}, title = {A generalization of {Vorono{\"\i}{\textquoteright}s} {Theorem} to algebraic lattices}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {727--740}, publisher = {Universit\'e Bordeaux 1}, volume = {22}, number = {3}, year = {2010}, doi = {10.5802/jtnb.742}, zbl = {1253.11072}, mrnumber = {2769341}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.742/} }
TY - JOUR AU - Okuda, Kenji AU - Yano, Syouji TI - A generalization of Voronoï’s Theorem to algebraic lattices JO - Journal de théorie des nombres de Bordeaux PY - 2010 SP - 727 EP - 740 VL - 22 IS - 3 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.742/ DO - 10.5802/jtnb.742 LA - en ID - JTNB_2010__22_3_727_0 ER -
%0 Journal Article %A Okuda, Kenji %A Yano, Syouji %T A generalization of Voronoï’s Theorem to algebraic lattices %J Journal de théorie des nombres de Bordeaux %D 2010 %P 727-740 %V 22 %N 3 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.742/ %R 10.5802/jtnb.742 %G en %F JTNB_2010__22_3_727_0
Okuda, Kenji; Yano, Syouji. 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. http://archive.numdam.org/articles/10.5802/jtnb.742/
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