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

  • Guangwei HuEmail author
  • Guangshi Lü


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 skth powers. We are able to generalize or improve previous results.

Mathematics Subject Classification (2010)

11E76 11F30 11P55 



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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanChina

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