Abstract
In this paper, we study the shifted convolution sums of the Fourier coefficients \(\lambda _\pi (1,\ldots ,1,n)\) and \(r_{s,k}(n)\) with \(k\ge 3\), where \(r_{s,k}(n)\) denotes the number of representations of the positive integer n as sums of s kth powers. We are able to generalize or improve previous results.
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Acknowledgements
The authors are very grateful to the referee for some extremely helpful remarks.
Funding
This work is supported in part by NSFC (Nos. 11771252, 11531008), IRT16R43, and the Taishan Scholar Project.
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Hu, G., Lü, G. Shifted convolution sums for \({{\varvec{SL}}}(m)\). manuscripta math. 163, 375–394 (2020). https://doi.org/10.1007/s00229-019-01166-1
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DOI: https://doi.org/10.1007/s00229-019-01166-1