A doubling integral for G2

TL;DR

This paper presents a novel integral representation for the standard L-function of G2 automorphic representations, applicable to both generic and non-generic cases, expanding the scope of L-function analysis.

Contribution

It introduces a new integral that unfolds to a matrix coefficient, enabling analysis of non-generic automorphic representations of G2.

Findings

Provides a new integral representation for G2 L-functions.

Applicable to both generic and non-generic automorphic representations.

Extends the scope of L-function analysis for exceptional groups.

Abstract

We introduce a new integral representation for the standard L-function of an irreducible cuspidal automorphic representation of the exceptional group G2, and also for the twist of this L-function by an arbitrary character. Because our construction unfolds to a matrix coefficient rather than a Whittaker function, it applies to non-generic representations as well as generic ones.