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A SHIFTED CONVOLUTION SUM OF 
$d_{3}$ AND THE FOURIER COEFFICIENTS OF HECKE–MAASS FORMS II
Published online by Cambridge University Press: 26 September 2019
Abstract
Let 
$d_{3}(n)$ be the divisor function of order three. Let 
$g$ be a Hecke–Maass form for 
$\unicode[STIX]{x1D6E4}$ with 
$\unicode[STIX]{x1D6E5}g=(1/4+t^{2})g$. Suppose that 
$\unicode[STIX]{x1D706}_{g}(n)$ is the 
$n$th Hecke eigenvalue of 
$g$. Using the Voronoi summation formula for 
$\unicode[STIX]{x1D706}_{g}(n)$ and the Kuznetsov trace formula, we estimate a shifted convolution sum of 
$d_{3}(n)$ and 
$\unicode[STIX]{x1D706}_{g}(n)$ and show that This corrects and improves the result of the author [‘Shifted convolution sum of 
$$\begin{eqnarray}\mathop{\sum }_{n\leq x}d_{3}(n)\unicode[STIX]{x1D706}_{g}(n-1)\ll _{t,\unicode[STIX]{x1D700}}x^{8/9+\unicode[STIX]{x1D700}}.\end{eqnarray}$$
$d_{3}$ and the Fourier coefficients of Hecke–Maass forms’, Bull. Aust. Math. Soc.92 (2015), 195–204].
- Type
- Research Article
- Information
- Copyright
- © 2019 Australian Mathematical Publishing Association Inc.
Footnotes
This project is supported by the National Natural Science Foundation of China (No. 11871193) and the Foundation of Henan University (No. CX3071A0780001).
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