On the local and global exterior square L-functions

TL;DR

This paper proves the equivalence of local exterior square L-functions constructed via integral representations and the Langlands-Shahidi method for certain representations of GL_n, with implications for local and global number theory.

Contribution

It establishes the coincidence of two different constructions of exterior square L-functions for GL_n, extending known results to all irreducible representations when n is even.

Findings

Local exterior square L-functions coincide for square integrable representations.

The equivalence extends to all irreducible representations when n is even.

Several local and global consequences are derived from this equivalence.

Abstract

We show that the local exterior square L-functions of GL_n constructed via the theory of integral representations by Jacquet and Shalika coincide with those constructed by the Langlands-Shahidi method for square integrable representations (and for all irreducible representations when n is even). We also deduce several local and global consequences.