Some Lambert series expansions of products of theta functions

被引：14

作者：

Williams, KS ^{[1
]}

机构：

[1] Carleton Univ, Sch Math & Stat, Ctr Res Algebra & Number Theory, Ottawa, ON K1S 5B6, Canada

来源：

RAMANUJAN JOURNAL | 1999年 / 3卷 / 04期

关键词：

theta functions; Lambert series; binary quadratic forms;

D O I：

10.1023/A:1009853106329

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let q be a complex number satisfying \ q \ < 1. The theta function phi(q) is defined by phi(q) = Sigma(x=-infinity)(infinity)q(x2). Ramanujan has given a number of Lambert series expansions such as [GRAPHICS] A formula is proved which includes this and other expansions as special cases.

引用

页码：367 / 384

页数：18

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