The Ramanujan Journal

, Volume 22, Issue 1, pp 101–117 | Cite as

Congruences modulo powers of 2 for a certain partition function

Article

Abstract

We study the divisibility properties of the coefficients c(n) defined by
$$\prod_{n=1}^\infty\frac{1}{(1-q^n)^2(1-q^{3n})^2}=\sum _{n=0}^\infty c(n)q^n.$$
An analogue of Ramanujan’s partition congruences is obtained for certain coefficients c(n) modulo powers of 2. Furthermore, an analogue of the identity that Hardy regarded as Ramanujan’s most beautiful is proved.
Ramanujan-type congruences Partition function 

Mathematics Subject Classification (2000)

05A15 05A30 05A40 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.University of Illinois at SpringfieldSpringfieldUSA
  2. 2.Institute of Information and Mathematical SciencesMassey UniversityAucklandNew Zealand

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