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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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 \(\mathrm {SL}_2({\mathbb {R}})\)