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On the non-vanishing of Poincaré series on the metaplectic group

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Abstract

In this paper, we study the K-finite matrix coefficients of integrable representations of the metaplectic cover of \( {\mathrm {SL}}_{2}({\mathbb {R}}) \) and give a result on the non-vanishing of their Poincaré series. We do this by adapting the techniques developed for \( {\mathrm {SL}}_{2}({\mathbb {R}}) \) by Muić to the case of the metaplectic group.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000, Zagreb, Croatia

    Sonja Žunar

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  1. Sonja Žunar
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Correspondence to Sonja Žunar.

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The author acknowledges Croatian Science Foundation Grant No. 9364.

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Žunar, S. On the non-vanishing of Poincaré series on the metaplectic group. manuscripta math. 158, 1–19 (2019). https://doi.org/10.1007/s00229-018-1011-6

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  • DOI: https://doi.org/10.1007/s00229-018-1011-6

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