Zagier duality for level $p$ weakly holomorphic modular forms

Paul Jenkins; Grant Molnar

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arXiv · 1709.10023

Zagier duality for level $p$ weakly holomorphic modular forms

Paul Jenkins·Grant Molnar

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Abstract

We prove Zagier duality between the Fourier coefficients of canonical bases for spaces of weakly holomorphic modular forms of prime level $p$ with $11 \leq p \leq 37$ with poles only at the cusp at $\infty$, and special cases of duality for an infinite class of prime levels. We derive generating functions for the bases for genus 1 levels.

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Paul Jenkins, Grant Molnar. 2018-02-08. Zagier duality for level $p$ weakly holomorphic modular forms. https://arxiv.org/abs/1709.10023

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