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Zagier duality for level p weakly holomorphic modular forms

Paul Jenkins,Grant Molnar

The Ramanujan Journal（2018）

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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 ≤ p ≤ 37 with poles only at the cusp at ∞ , 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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Key words
Modular forms, Zagier duality, Prime level, Generating function, Canonical basis, Primary 11F30, Secondary 11F37
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