Congruence properties for the partition function

Proceedings of the National Academy of Sciences of the United States of America
S Ahlgren, K Ono

Abstract

Eighty years ago, Ramanujan conjectured and proved some striking congruences for the partition function modulo powers of 5, 7, and 11. Until recently, only a handful of further such congruences were known. Here we report that such congruences are much more widespread than was previously known, and we describe the theoretical framework that appears to explain every known Ramanujan-type congruence.

Citations

Dec 19, 2008·Proceedings of the National Academy of Sciences of the United States of America·Amanda Folsom, Ken Ono
Dec 24, 2010·Proceedings of the National Academy of Sciences of the United States of America·Ken Ono
Mar 16, 2007·Proceedings of the National Academy of Sciences of the United States of America·Kathrin Bringmann, Ken Ono
Oct 12, 2005·Proceedings of the National Academy of Sciences of the United States of America·Karl Mahlburg
Oct 19, 2005·Proceedings of the National Academy of Sciences of the United States of America·George E Andrews, Ken Ono
Aug 29, 2020·Proceedings of the National Academy of Sciences of the United States of America·Olivia BeckwithOlav K Richter

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