TY  - BOOK
AU  - Pitale,Ameya
AU  - Saha,Abhishek
AU  - Schmidt,Ralf
TI  - Transfer of Siegel cusp forms of degree 2
T2  - Memoirs of the American Mathematical Society
SN  - 9780821898567 (pbk. : acidfree paper)
U1  - 510 23
PY  - 2014///
CY  - Providence :      
PB  - American Mathematical Society,       
KW  - Cusp forms (Mathematics)
KW  - Siegel domains
KW  - Modular groups
N1  - "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
N2  - 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?
ER  -