• On Whittaker models and the vanishing of Fourier coefficients of cusp forms

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      https://www.ias.ac.in/article/fulltext/pmsc/097/01-03/0067-0074

    • Keywords

       

      Whittaker models; cusp forms; automorphic cuspidal representations

    • Abstract

       

      The purpose of this paper is to construct examples of automorphic cuspidal representations which possess a ψ-Whittaker model even though their ψ-Fourier coefficients vanish identically. This phenomenon was known to be impossible for the groupGL(n), but in general remained an open problem. Our examples concern the metaplectic group and rely heavily upon J L Waldspurger’s earlier analysis of cusp forms on this group.

    • Author Affiliations

       

      Stephen Gelbart1 David Soudry2

      1. Department of Mathematics, The Weizmann Institute of Science, Rehovot - 76100, Israel
      2. Department of Mathematics, Tel-Aviv University, Tel Aviv - 69978, Israel
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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