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Transfer of Siegel cusp forms of degree 2
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Transfer of Siegel cusp forms of degree 2
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Transfer of Siegel cusp forms of degree 2
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eBook
Transfer of Siegel cusp forms of degree 2
2014
Overview
Let \\pi be the automorphic representation of \\textrm{GSp}_4(\\mathbb{A}) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and \\tau be an arbitrary cuspidal, automorphic representation of \\textrm{GL}_2(\\mathbb{A}). Using Furusawa's integral representation for \\textrm{GSp}_4\\times\\textrm{GL}_2 combined with a pullback formula involving the unitary group \\textrm{GU}(3,3), the authors prove that the L-functions L(s,\\pi\\times\\tau) are \"nice\". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations \\pi have a functorial lifting to a cuspidal representation of \\textrm{GL}_4(\\mathbb{A}). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of \\pi to a cuspidal representation of \\textrm{GL}_5(\\mathbb{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 \\textrm{GSp}_4\\times\\textrm{GL}_1 and \\textrm{GSp}_4\\times\\textrm{GL}_2.
Publisher
American Mathematical Society
Subject
ISBN
9780821898567, 0821898566
