Partitions and Hecke images

2025/09/25 by Breuer, Florian, Pazuki, Fabien
#05A17 #11F11 #11P82 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.21603

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.

Citations

• Explicit bounds on the coefficients of the modular polynomials and the size of X₀(N)
• Explicit bounds on the coefficients of modular polynomials for the elliptic j-invariant

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• Modular Forms and Certain ₂F₁(1) Hypergeometric Series