Congruence properties for the partition function

Proc Natl Acad Sci U S A. 2001 Nov 6;98(23):12882-4. doi: 10.1073/pnas.191488598. Epub 2001 Oct 23.

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.