Exterior Cube L-function for GL_6

Abstract

In this paper, we study the analytic properties of exterior cube L-function for the group GL_6 introduced by Ginzburg and Rallis. More precisely, for a cusp form of GL_6(A), we can associate to each unramified representation a semisimple conjugacy class in the L-group, then we can define the local L-function. If let S be a finite set of places, thus we can define the partial exterior L-function. Our goal is to show that the partial L-function is entire for all characters and for all generic cusp forms on GL_6 except for finite many poles. We will also generalize the analytic properties to the general cases.