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Some new identities involving Dedekind sums and the Ramanujan sum

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Abstract

The main purpose of this paper is to introduce new sums that are analogous to Dedekind sums. Using analysis and properties of Dirichlet \(L\)-functions, we study mean values for these new sums, and give a sharper mean value formula for it.

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Acknowledgments

The authors would like to thank the referee for his very helpful and detailed comments, which have significantly improved the presentation of this paper.

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, Shaanxi, P.R.China

    Di Han & Wenpeng Zhang

Authors
  1. Di Han
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  2. Wenpeng Zhang
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Correspondence to Di Han.

Additional information

This work is supported by the N.S.F.(11371291) of P.R.China and G.I.C.F.(YZZ13071) of NWU.

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Han, D., Zhang, W. Some new identities involving Dedekind sums and the Ramanujan sum. Ramanujan J 35, 253–262 (2014). https://doi.org/10.1007/s11139-014-9591-6

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  • DOI: https://doi.org/10.1007/s11139-014-9591-6

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