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arXiv · 2309.00243

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

Amrinder Kaur·Ayyadurai Sankaranarayanan
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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 $L_{f \times f}(s)$.

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Amrinder Kaur, Ayyadurai Sankaranarayanan. 2023-09-01. On the Rankin-Selberg $L$-function related to the Godement-Jacquet $L$-function II. https://arxiv.org/abs/2309.00243

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