On the Rankin--Selberg $L$-function relatedto the Godement--Jacquet $L$-function II
Copyright policy )On the Rankin--Selberg $L$-function relatedto the Godement--Jacquet $L$-function II
In this paper, we consider the $k$-th Riesz mean for the coefficients of the Rankin-Selberg $L$-function $L_{f \times f}(s)$ related to the Godement-Jacquet $L$-function with respect to $SL(n,\mathbb{Z})$. We establish an asymptotic formula for the $k$-th Riesz mean with an improved range and a better error term. As a result, we get an asymptotic relation for the partial sum of the coefficients of $L_{f \times f}(s)$.
- University of Hyderabad India
Fourier coefficients of automorphic forms, Applications of automorphic functions and forms to multiplicative problems, Mathematics - Number Theory, Langlands \(L\)-functions; one variable Dirichlet series and functional equations, Riesz mean asymptotic formula, FOS: Mathematics, Godement-Jacquet \(L\)-function, Number Theory (math.NT), Hecke-Maass form, 11F30, 11N75, Rankin-Selberg \(L\)-function
Fourier coefficients of automorphic forms, Applications of automorphic functions and forms to multiplicative problems, Mathematics - Number Theory, Langlands \(L\)-functions; one variable Dirichlet series and functional equations, Riesz mean asymptotic formula, FOS: Mathematics, Godement-Jacquet \(L\)-function, Number Theory (math.NT), Hecke-Maass form, 11F30, 11N75, Rankin-Selberg \(L\)-function
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