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Transfer of Siegel cusp forms of degree 2 / Ameya Pitale, Abhishek Saha and Ralf Schmidt.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 232, no 1090.Publication details: Providence : American Mathematical Society, c2014.Description: v, 107 p. ; 25 cmISBN:
  • 9780821898567 (pbk. : acidfree paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
Introduction-- Notation-- 1. Distinguished vectors in local representations-- 2. Global L-functions for GSp4 X GL2-- 3. The pullback formula-- 4. Holomorphy of global L-functions for GSp4 X GL2-- 5. Applications-- Bibliography.
Summary: Let p be the automorphic representation of GSp4 ( A ) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and t be an arbitrary cuspidal, automorphic representation of GL? ( A ). Using Furusawa's integral representation for GSp? X GL? combined with a pullback formula involving the unitary group GU (3,3), the authors prove that the L-functions L(s, p X t are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations p have a functorial lifting to a cuspidal representation of GL? ( A ). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of p to a cuspidal representation of GL5 ( A ). As an application, the authors obtain analytic properties of various L-functions related to full level Siegel cusp forms. They also obtain special value results for GSp? X GL? and GSp4 X GL?.
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"November 2014, volume 232, number 1090 (second of 6 numbers)"

Includes bibliographical references (pages 103-107).

Introduction--
Notation--
1. Distinguished vectors in local representations--
2. Global L-functions for GSp4 X GL2--
3. The pullback formula--
4. Holomorphy of global L-functions for GSp4 X GL2--
5. Applications--
Bibliography.

Let p be the automorphic representation of GSp4 ( A ) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and t be an arbitrary cuspidal, automorphic representation of GL? ( A ). Using Furusawa's integral representation for GSp? X GL? combined with a pullback formula involving the unitary group GU (3,3), the authors prove that the L-functions L(s, p X t are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations p have a functorial lifting to a cuspidal representation of GL? ( A ). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of p to a cuspidal representation of GL5 ( A ). As an application, the authors obtain analytic properties of various L-functions related to full level Siegel cusp forms. They also obtain special value results for GSp? X GL? and GSp4 X GL?.

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