Non-vanishing of certain integral representations

Abstract

In this paper, we prove that there exist Whittaker and Schwartz functions such that the local Flicker integrals are non-vanishing for all complex values of $s$, and the local Bump-Friedberg integrals are non-vanishing for all complex pairs $(s_1,s_2)$. As a corollary, we determine the potential locations of poles for their corresponding partial $L$-functions.

14 pages, to appear in The Ramanujan Journal