An upper bound on the number of perfect quadratic forms

被引：1
|
作者：
van Woerden, W. P. J. [1 ]
机构：
[1] CWI, Cryptol Grp, Amsterdam, Netherlands
来源：
ADVANCES IN MATHEMATICS | 2020年 / 365卷
关键词：
Perfect quadratic form; Perfect lattice; COMPLETE ENUMERATION;
D O I：
10.1016/j.aim.2020.107031
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In a recent publication Roland Bacher showed that the number p(d) of non-similar perfect d-dimensional quadratic forms satisfies e(Omega(d)) < p(d) < e(O(d3 log (d))). We improve the upper bound to e(O(d2 log (d))) by a volumetric argument based on Voronoi's first reduction theory. (C) 2020 Elsevier Inc. All rights reserved.
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页数：12
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