Ramanujan’s congruences for partitions modulo $5, 7$ and $11$

Don Zagier - Ramanujan’s congruences for partitions modulo $5, 7$ and $11$

hrj:17901 - Hardy-Ramanujan Journal, April 27, 2026, Volume 48 - 2025 - https://doi.org/10.46298/hrj.2026.17901

Ramanujan’s congruences for partitions modulo $5, 7$ and $11$Article

Authors: Don Zagier ¹

We obtain short and uniform proofs of Ramanujan's partition congruences modulo $5, 7$ and $11$.

Volume: Volume 48 - 2025

Published on: April 27, 2026

Accepted on: April 27, 2026

Submitted on: April 2, 2026

Keywords: 11P83, [MATH]Mathematics [math], [en] Modular forms, Dedekind eta function, partition congruences