Memoirs of the American Mathematical Society 2014; 107 pp; softcover Volume: 232 ISBN10: 0821898566 ISBN13: 9780821898567 List Price: US$75 Individual Members: US$45 Institutional Members: US$60 Order Code: MEMO/232/1090
 Let \(\pi\) be the automorphic representation of \(\textrm{GSp}_4(\mathbb{A})\) generated by a full level cuspidal Siegel eigenform that is not a SaitoKurokawa 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 PiatetskiShapiro then implies that such representations \(\pi\) have a functorial lifting to a cuspidal representation of \(\textrm{GL}_4(\mathbb{A})\). Combined with the exteriorsquare 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 \(\textrm{GSp}_4\times\textrm{GL}_2\). Table of Contents  Introduction
 Notation
 Distinguished vectors in local representations
 Global \(L\)functions for \(\textrm{GSp}_4\times\textrm{GL}_2\)
 The pullback formula
 Holomorphy of global \(L\)functions for \(\textrm{GSp}_4\times\textrm{GL}_2\)
 Applications
 Bibliography
