Identities and congruences for the general partition and Ramanujan's tau functions

被引：21

作者：

Baruah, Nayandeep Deka ^{[1
]}

Sarmah, Bipul Kumar ^{[2
]}

机构：

[1] Tezpur Univ, Dept Math Sci, Sonitpur 784028, Assam, India

[2] Tezpur Univ, Dept Math Sci, Sonitpur 784028, Assam, India

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2013年 / 44卷 / 05期

关键词：

Partition; partition congruences; Rogers-Ramanujan continued fraction; Ramanujan's theta function; POWERS;

D O I：

10.1007/s13226-013-0034-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present some identities and congruences for the general partition function p (r) (n). In particular, we deduce some known identities for Ramanujan's tau function and find simple proofs of Ramanujan's famous partition congruences for modulo 5 and 7. Our emphasis throughout this paper is to exhibit the use of Ramanujan's theta functions to generate identities and congruences for general partition function.

引用

页码：643 / 671

页数：29

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