Relations between the ranks and cranks of partitions

被引：78

作者：

Atkin, AOL

Garvan, FG

机构：

[1] Univ Illinois, Dept Math, Chicago, IL 60607 USA

[2] Univ Florida, Dept Math, Gainesville, FL 32611 USA

来源：

RAMANUJAN JOURNAL | 2003年 / 7卷 / 1-3期

基金：

美国国家科学基金会;

关键词：

partitions; rank; crank; Ramanujan congruences; Eisenstein series; modular forms;

D O I：

10.1023/A:1026219901284

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

New identities and congruences involving the ranks and cranks of partitions are proved. The proof depends on a new partial differential equation connecting their generating functions.

引用

页码：343 / 366

页数：24

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