Multiplicative property of representation numbers of ternary quadratic forms

被引：0

作者：

Lu, Wei ^{[1
]}

Qin, Hourong ^{[2
]}

机构：

[1] Southeast Univ, Sch Math, Nanjing 211189, Jiangsu, Peoples R China

[2] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

来源：

MANUSCRIPTA MATHEMATICA | 2018年 / 156卷 / 3-4期

关键词：

MODULAR-FORMS; SERIES; WEIGHT;

D O I：

10.1007/s00229-017-0964-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f be a positive definite integral ternary quadratic form and its theta function. For any fixed square-free positive integer t with , we define . For the case when and , Hurwitz proved that is multiplicative and he gave its expression. Cooper and Lam proved four similar formulas and proposed a conjecture for some other cases. Using the results given in this paper, we can check the multiplicative property of for many cases. All cases in Cooper and Lam's conjecture are included in ours.

引用

页码：457 / 467

页数：11

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