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On the non-vanishing of L-functions associated to cusp forms of half-integral weight

Abstract

We prove a strengthening of Muić’s integral non-vanishing criterion for Poincaré series on unimodular locally compact Hausdorff groups and use it to prove a result on non-vanishing of L-functions associated to cusp forms of half-integral weight.

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Acknowledgements

This paper grew out of my PhD thesis. I would like to thank my advisor, Goran Muić, for his encouragement, support, and many discussions. I would also like to thank Petar Bakić for some useful comments.

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Correspondence to Sonja Žunar.

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The author acknowledges support from the Croatian Science Foundation Grant No. 9364.

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Žunar, S. On the non-vanishing of L-functions associated to cusp forms of half-integral weight. Ramanujan J 51, 455–477 (2020). https://doi.org/10.1007/s11139-019-00135-2

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  • DOI: https://doi.org/10.1007/s11139-019-00135-2

Keywords

  • L-functions
  • Cusp forms of half-integral weight
  • Non-vanishing of Poincaré series
  • Metaplectic cover of \(\mathrm {SL}_2({\mathbb {R}})\)

Mathematics Subject Classification

  • 11F37