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Transfer of Siegel cusp forms of degree $2$


About this Title

Ameya Pitale, Abhishek Saha and Ralf Schmidt

Publication: Memoirs of the American Mathematical Society
Publication Year: 2014; Volume 232, Number 1090
ISBNs: 978-0-8218-9856-7 (print); 978-1-4704-1893-9 (online)
DOI: http://dx.doi.org/10.1090/memo/1090
Published electronically: February 19, 2014

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Table of Contents


Chapters

  • Introduction
  • Notation
  • Chapter 1. Distinguished vectors in local representations
  • Chapter 2. Global $L$-functions for $\textup {GSp}_4\times \textup {GL}_2$
  • Chapter 3. The pullback formula
  • Chapter 4. Holomorphy of global $L$-functions for $\textup {GSp}_4 \times \textup {GL}_2$
  • Chapter 5. Applications

Abstract


Let be the automorphic representation of generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and be an arbitrary cuspidal, automorphic representation of . Using Furusawa's integral representation for combined with a pullback formula involving the unitary group , we prove that the -functions are “nice”. The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations have a functorial lifting to a cuspidal representation of . Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of to a cuspidal representation of . As an application, we obtain analytic properties of various -functions related to full level Siegel cusp forms. We also obtain special value results for and .

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