Zagier duality for level $p$ weakly holomorphic modular forms

Grant Molnar; Paul Jenkins

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Zagier duality for level $p$ weakly holomorphic modular forms

Paul Jenkins, Grant Molnar

Number Theory · Submitted 28 Sep 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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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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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	result 0.55	0.96	0.92	asserted 1.00
s1	We derive generating functions for the bases for genus 1 levels.	contribution 0.56	0.91	0.06	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original 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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