Arithmetic of the Partition Function

M. Ram Murty and V. Kumar Murty
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M. Ram Murty: Queen’s University, Department of Mathematics and Statistics
V. Kumar Murty: University of Toronto, Department of Mathematics

Chapter Chapter 7 in The Mathematical Legacy of Srinivasa Ramanujan, 2013, pp 109-117 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-81-322-0770-2_7

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