Transfer of Siegel Cusp Forms of Degree 2
نویسندگان
چکیده
Let 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 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-functions related to full level Siegel cusp forms. We also obtain special value results for GSp4 ×GL1 and GSp4 ×GL2. Received by the editor February 6, 2012, and, in revised form, January 5, 2013. Article electronically published on February 19, 2014. DOI: http://dx.doi.org/10.1090/memo/109
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