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Zagier duality for level p weakly holomorphic modular forms

The Ramanujan Journal volume 50, pages 93–109 (2019)Cite this article

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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Corresponding author

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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  • DOI: https://doi.org/10.1007/s11139-018-0009-8

Keywords

  • Modular forms
  • Zagier duality
  • Prime level
  • Generating function
  • Canonical basis

Mathematics Subject Classification

  • Primary 11F30
  • Secondary 11F37