On the Rankin-Selberg $L$-function related to the Godement-Jacquet $L$-function II

Amrinder Kaur; Ayyadurai Sankaranarayanan

On the Rankin-Selberg $L$-function related to the Godement-Jacquet $L$-function II

Number Theory 2023-09-04 v1

Authors: Amrinder Kaur , Ayyadurai Sankaranarayanan

Abstract

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 $L_{f \times f}(s)$ .

Keywords

rankin-selberg l-function godement-jacquet l-function riesz mean asymptotic formula error term partial sum

Cite

@article{arxiv.2309.00243,
  title  = {On the Rankin-Selberg $L$-function related to the Godement-Jacquet $L$-function II},
  author = {Amrinder Kaur and Ayyadurai Sankaranarayanan},
  journal= {arXiv preprint arXiv:2309.00243},
  year   = {2023}
}

On the Rankin-Selberg $L$-function related to the Godement-Jacquet $L$-function II

Abstract

Keywords

Cite

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