Abstracts Mathematics

L-function for Sp(4)xGL(2) via a non-unique model

by Pan Yan

We prove a conjecture of Ginzburg and Soudry on an integral representation for the tensor product partial L-function attached to a pair of irreducible automorphic cuspidal representations of Sp_4(A) and GL_2(A), which is derived from the twisted doubling method of Cai, Friedberg, Ginzburg and Kaplan. We show that the integral unfolds to a non-unique model and analyze it using the New Way method of Piatetski-Shapiro and Rallis. As applications, we determine the poles of the tensor product partial L-function and relate the existence of the poles to the non-vanishing of certain period integrals. Moreover, for certain family of cuspidal representations of GL_2(A), we prove that the tensor product partial L-function is holomorphic.