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

Abstract: The theory of L-functions of automorphic forms or automorphic representations is a central topic in modern number theory. A fruitful way to study L-functions is through an integral formula, commonly referred to as an integral representation. The most common examples of Eulerian integrals are the ones which unfold to a unique model such as the Whittaker model. Integrals which unfold to non-unique models fall outside of this paradigm, and there are only a few such examples which are known to represent L-functions. In this talk, we prove a conjecture of Ginzburg and Soudry [IMRN, 2020] on an integral representation for the tensor product partial L-function for Sp(4)×GL(2) 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.

number theory

Audience: researchers in the topic

University of Arizona Algebra and Number Theory Seminar