Transfer of Siegel cusp forms of degree 2 - Pitale, Ameya, 1977-; Saha, Abhishek, 1982-; Schmidt, Ralf, 1968- (Memoirs of the American Mathematical Society, 2014)
Let π be the automorphic representation of GSp_4(\mathbb{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 GL_2(\mathbb{A}). Using Furusawa's integral representation for GSp_4×GL_2 combined with a pullback formula involving the unitary group GU(3,3), the authors 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 lift