Ternary quadratic forms representing the same integers

被引：1

作者：

Ju, Jangwon ^{[1
]}

机构：

[1] Univ Ulsan, Dept Math, Ulsan 44610, South Korea

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2022年 / 18卷 / 09期

基金：

新加坡国家研究基金会;

关键词：

Representations of ternary quadratic forms; Kaplansky's conjecture;

D O I：

10.1142/S1793042122500981

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1997, Kaplansky conjectured that if two positive definite ternary quadratic forms with integer coefficients have perfectly identical integral representations, then they are isometric, both regular, or included either of two families of ternary quadratic forms. In this paper, we prove the existence of pairs of ternary quadratic forms representing the same integers which are not contained in Kaplansky's list.

引用

页码：1921 / 1928

页数：8

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