The Rankin–Selberg integral with a non-unique model for the standard -function of

Abstract

Abstract Let $\mathcal{L}^{S}\left (s,\pi ,{\mathfrak{st}}\right )$ be a partial $\mathcal{L}$ -function of degree $7$ of a cuspidal automorphic representation $\pi $ of the exceptional group $G_2$ . In this paper we construct a Rankin–Selberg integral for representations having a certain Fourier coefficient.