Rankin-Selberg integral with Non-unique model for the standard L-function of $G_2$

TL;DR

This paper constructs a Rankin-Selberg integral for a specific L-function associated with the exceptional group G_2, focusing on representations with particular Fourier coefficients, advancing the understanding of automorphic L-functions.

Contribution

It introduces a novel Rankin-Selberg integral for the standard L-function of G_2 using a non-unique model, expanding methods for analyzing automorphic forms on exceptional groups.

Findings

Constructed a new integral representation for L^S(, ext{st}) of G_2

Extended Rankin-Selberg methods to non-unique models

Provided insights into Fourier coefficients of automorphic representations

Abstract

Let L^S(\pi,s,st) be a partial L-function of degree 7 of a cuspidal automorphic representation \pi of the exceptional group G_2. Here we construct a Rankin-Selberg integral for representations having certain Fourier coefficient.