Notes on general divisor problems related to Maass cusp forms. (English) Zbl 07692669
Summary: 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 \[\sum_{n\le x}\lambda_{k,f}(n^j):=\sum_{n=n_1n_2\cdots n_k\le x}\lambda_f(n_1^j)\cdots \lambda_f(n_k^j),\] 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 D. Wang [Acta Math. Hung. 153, No. 2, 509–523 (2017; Zbl 1413.11112)].
MSC:
| 11N37 | Asymptotic results on arithmetic functions |
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
Citations:
Zbl 1413.11112References:
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