Partitions and Hecke images
Number Theory
2025-09-29 v1 Combinatorics
Abstract
We obtain a new family of relations satisfied by the partition function. In contrast with most partition relations, these involve non-trivial roots of unity. We present two proofs, one using the fact that the discriminant modular form is a multiplicative Hecke eigenform, and one direct proof using q-series.
Cite
@article{arxiv.2509.21603,
title = {Partitions and Hecke images},
author = {Florian Breuer and Fabien Pazuki},
journal= {arXiv preprint arXiv:2509.21603},
year = {2025}
}