Download or read book Transfer of Siegel Cusp Forms of Degree 2 written by Ameya Pitale and published by . This book was released on 2014 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let π 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 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 L-functions related to full level Siegel cusp forms. We also obtain special value results for GSp4 × GL1 and GSp4 × GL2.