Triple product $L$-functions related to $\mathrm{GL}(6)$ automorphic forms

Abstract

In this paper, we study the distribution of Fourier coefficients of triple product $L$-functions associated with certain $\mathrm{GL}(6)$ automorphic forms. More precisely, we derive the asymptotic formulas for the first moment of Fourier coefficients of the automorphic $L$-functions attached to these $\mathrm{GL}(6)$ forms.