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A generalization on the difference between an integer and its inverse modulo Q

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Abstract

The main purpose of this paper is to use the properties of the Gauss sums, primitive characters and the mean value of Dirichlet L-functions to study the hybrid mean value of the error term E(n, 1, c, q) and the hyper-Kloosterman sums K(h, n+1, q), the asymptotic property of the mean square value Σ p c=1 E 2(n, 1, c, p), and give two interesting mean value formulae.

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Authors and Affiliations

  1. Department of Mathematics, Northwest University, Xi’an, 710069, P. R. China

    Tian Ping Zhang

  2. College of Mathematics and Information Science, Shannxi Normal University, Xi’an, 710062, P. R. China

    Tian Ping Zhang

  3. Department of Mathematics, Northwest University, Xi’an, 710069, P. R. China

    Wen Peng Zhang

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  1. Tian Ping Zhang
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  2. Wen Peng Zhang
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Correspondence to Tian Ping Zhang.

Additional information

This work is supported by the N.S.F. (10271093, 60472068) and P.N.S.F of P. R. China

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Zhang, T.P., Zhang, W.P. A generalization on the difference between an integer and its inverse modulo Q . Acta. Math. Sin.-English Ser. 24, 215–222 (2008). https://doi.org/10.1007/s10114-007-0942-8

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  • DOI: https://doi.org/10.1007/s10114-007-0942-8

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