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Notes on general divisor problems related to Maass cusp forms

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Abstract

Let f be a Maass cusp form and \(\lambda _f(n)\) be the n-th normalized Fourier coefficients of f at the cusp \(\infty \). In this paper, we are interested in estimating the sum

$$\begin{aligned} \sum _{n\le x}\lambda _{k,f} (n^j):=\sum _{n={n_1}{n_2}\dots {n_k}\le x} \lambda _f(n_1^j)\cdots \lambda _f(n_k^j), \end{aligned}$$

where \(k \ge 2 \) is an integer, and \(j=1,2,3,4.\) In particular, when \(k=3\), \( j=1\) we improve a previous result of Wang (Acta Math Hungar 153:509–523, 2017).

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Acknowledgements

The author would like to thank the referee for valuable suggestions and comments. This work is supported by the National Natural Science Foundation of China (Grant No. 12171286) and the Natural Science Foundation of Tianjin City (Grant No. 19JCQNJC14200).

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  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250358, Shandong, China

    Huafeng Liu

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Liu, H. Notes on general divisor problems related to Maass cusp forms. Period Math Hung 86, 552–563 (2023). https://doi.org/10.1007/s10998-022-00490-6

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