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Arithmetic of the Partition Function

  • M. Ram Murty
  • V. Kumar Murty
Chapter

Abstract

The partition function p(n) enjoys some remarkable congruence properties. Most notable are the celebrated Ramanujan congruences p(5n+4)≡0 (mod 5), p(7n+5)≡0 (mod 7), and p(11n+6)≡0 (mod 11). After a discussion of the rationale behind these congruences, we discuss generalizations and open questions regarding the behaviour of the partition function.

Keywords

Partition Function Modular Form Eisenstein Series Cusp Form Congruence Modulo 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer India 2013

Authors and Affiliations

  • M. Ram Murty
    • 1
  • V. Kumar Murty
    • 2
  1. 1.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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