Transfer of Siegel Cusp Forms of Degree 2
Seiten
2014
American Mathematical Society (Verlag)
978-0-8218-9856-7 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-9856-7 (ISBN)
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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?.
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?.
Ameya Pitale, University of Oklahoma, Norman, Oklahoma, USA. Abhishek Saha, University of Bristol, United Kingdom. Ralf Schmidt, University of Oklahoma, Norman, Oklahoma, USA.
Introduction
Notation Distinguished vectors in local representations
Global L-functions for GSp? X GL?
The pullback formula
Holomorphy of global L-functions for GSp? X GL?
Applications
Bibliography
Erscheint lt. Verlag | 30.10.2014 |
---|---|
Reihe/Serie | Memoirs of the American Mathematical Society |
Verlagsort | Providence |
Sprache | englisch |
Maße | 178 x 254 mm |
Gewicht | 188 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
ISBN-10 | 0-8218-9856-6 / 0821898566 |
ISBN-13 | 978-0-8218-9856-7 / 9780821898567 |
Zustand | Neuware |
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