The Dirichlet Series for the Exterior Square $L$-function on GL(n)

TL;DR

This paper provides an elementary derivation of the Jacquet-Shalika construction for the exterior square L-function on GL(n), expressing it as a classical Dirichlet series in Fourier coefficients.

Contribution

It offers a simplified, elementary derivation of the exterior square L-function construction, making the approach more accessible.

Findings

Derivation of the exterior square L-function as a Dirichlet series

Simplification of the Jacquet-Shalika construction

Enhanced understanding of Fourier coefficient relations

Abstract

We present an elementary derivation of the Jacquet-Shalika construction for the exterior square L-function on GL(n), as a classical Dirichlet series in the Fourier coefficients $A(m_1,...,m_{n-1})$.