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Zagier duality for level p weakly holomorphic modular forms

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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 \(11 \le p \le 37\) 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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Acknowledgements

The authors thank Scott Ahlgren, Nick Andersen, Michael Griffin, Ben Kane, and Jeremy Rouse for their invaluable insights.

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Authors and Affiliations

  1. Brigham Young University, Provo, UT, USA

    Paul Jenkins & Grant Molnar

Authors
  1. Paul Jenkins
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  2. Grant Molnar
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Correspondence to Grant Molnar.

Additional information

This work was partially supported by a Grant from the Simons Foundation (\(\# 281876\) to Paul Jenkins).

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Jenkins, P., Molnar, G. Zagier duality for level p weakly holomorphic modular forms. Ramanujan J 50, 93–109 (2019). https://doi.org/10.1007/s11139-018-0009-8

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