Congruence properties for the partition function

2001/10/23 by Scott Ahlgren, Ken Ono · 1 voice · 4 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research

paper · doi:10.1073/pnas.191488598

openalex publication_date 2001/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

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

• On Modular Forms of Half Integral Weight

Cited by

• A family of mock theta functions of weights 1/2 and 3/2 and their congruence properties
• Lifting cusp forms to Maass forms with an application to partitions
• Arithmetic properties of the partition function
• Partition function (number theory) [wikipedia]

Discussions

• TIL that not only does Ken Ono have 14 number theory papers in the Proceedings of the National Academy of Sciences (!), he has had two of them feature on the cover! https://doi.org/10.1073/pnas.19148 [bsky, 0 points, 1 comments]