Shifted convolution sums for \({{\varvec{SL}}}(m)\)


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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The authors are very grateful to the referee for some extremely helpful remarks.


This work is supported in part by NSFC (Nos. 11771252, 11531008), IRT16R43, and the Taishan Scholar Project.

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Correspondence to Guangwei Hu.

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Hu, G., Lü, G. Shifted convolution sums for \({{\varvec{SL}}}(m)\). manuscripta math. 163, 375–394 (2020).

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Mathematics Subject Classification (2010)

  • 11E76
  • 11F30
  • 11P55