Polynesian Journal of Mathematics

Volume 3, Issue 1

Partitions and Hecke images

Florian Breuer and Fabien Pazuki

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.

Keywords: Partitions, modular forms, Hecke images, $q$-series.

Citation:

Florian Breuer and Fabien Pazuki. Partitions and Hecke images. Polynesian Journal of Mathematics, Volume 3, Issue 1, Pages 1–7. (March 2026) DOI: 10.69763/polyjmath.3.1

Export to BibTeX

Milestones:

Received 7 Oct 2025
Revised 25 Mar 2026
Accepted 26 Mar 2026
Published 28 Mar 2026
Communicated by Roger Oyono

The above content is published under the terms of the Creative Commons Attribution 4.0 International license.