RAMANUJAN'S CONGRUENCES FOR THE PARTITION FUNCTION MODULO 5, 7, AND 11-Reference-Cited by-同舟云学术

RAMANUJAN'S CONGRUENCES FOR THE PARTITION FUNCTION MODULO 5, 7, AND 11

Published:2007-09 Issue:03 Volume:03 Page:349-354
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

BERNDT BRUCE C.¹

Affiliation:

1. Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA

Abstract

Using Ramanujan's differential equations for Eisenstein series and an idea from Ramanujan's unpublished manuscript on the partition function p(n) and the tau function τ(n), we provide simple proofs of Ramanujan's congruences for p(n) modulo 5, 7, and 11.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042107000961

Reference9 articles.

1. Ramanujan’s Unpublished Manuscript on the Partition and Tau Functions with Proofs and Commentary

2. Congruence properties of functions related to the partition function

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