Hecke equivariance of the divisor map

2025/05/03 by Daeyeol Jeon, Soon-Yi Kang, Jeon, Daeyeol +5 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2505.01702

Abstract

We study the multiplicative Hecke operators acting on the space of meromorphic modular forms, and show that the divisor map to divisors on X₀(N) is a Hecke equivariant map. As applications, we investigate the divisor sum formula of Bruinier-Kohnen-Ono and more general Rohrlich-type divisor sums for polyharmonic Maass forms, discussing several implications for the Hecke action and its relation to the self-adjointness of the Hecke operators.

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• The Fourier coefficients and singular moduli of the elliptic modular function j(τ), revisited

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