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Sum of the triple divisor function and Fourier coefficients of $SL(3,\mathbb{Z})$ Hecke-Maass forms over quadratics

Authors :
Chanana, Himanshi
Singh, Saurabh Kumar
Publication Year :
2023
Publisher :
arXiv, 2023.

Abstract

Let $\mathcal{A}(n)$ be the $(1,n)-th$ Fourier coefficients of $SL(3,\mathbb{Z})$ Hecke-Maass cusp form i.e. $\Lambda(1,n)$ or the triple divisor function $d_3(n)$, which is the number of solutions of the equation $r_1r_2r_3 = n$ with $r_1, r_2, r_3 \in \mathbb{Z}^+.$ We establish estimates for \begin{equation*} \sum_{1 \leq n_1,n_2\leq X} \mathcal{A}(Q(n_1,n_2)) \end{equation*} where $Q(x,y) \in \mathbb{Z}[x,y]$ is a symmetric positive definite quadratic form.<br />Comment: This article is of 19 pages. Comments/Suggestions are welcome

Details

Database :
OpenAIRE
Accession number :
edsair.doi.dedup.....28114e1131e4ac99112d4cf39d6ed9f2
Full Text :
https://doi.org/10.48550/arxiv.2303.15856