Transfer of Siegel cusp forms of degree 2

Ameya Pitale, Abhishek Saha, Ralf Schmidt

Research output: Contribution to journalArticle (Academic Journal)peer-review

11 Citations (Scopus)
234 Downloads (Pure)

Abstract

Let π be the automorphic representation of GSp4(A) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and τ be an arbitrary cuspidal, automorphic representation of GL2(A). Using Furusawa’s integral representation for GSp4×GL2 combined with a pullback formula involving the unitary group GU(3,3), we prove that the L-functions L(s,π×τ) are “nice”. The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations π have a functorial lifting to a cuspidal representation of GL4(A). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of π to a cuspidal representation of GL5(A). As an application, we obtain analytic properties of various L-functions related to full level Siegel cusp forms. We also obtain special value results fforms. We also obtain special value results for GSp4×GL1 and GSp4×GL2.
Original languageEnglish
Article number1090
Number of pages120
JournalMemoirs of the American Mathematical Society
Volume232
Issue number1090
Early online date19 Feb 2014
DOIs
Publication statusPublished - Nov 2014

Keywords

  • Cusp forms (Mathematics)
  • Siegel domains
  • Modular groups

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