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Mean Value on the Difference Between a Quadratic Residue and Its Inverse Modulo p

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Abstract

The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet L-functions to study the asymptotic property of the difference between a quadratic residue and its inverse modulo p (a prime), and to give an interesting hybrid mean value formula.

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Authors and Affiliations

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

    Hua Ning Liu & Wen Peng Zhang

Authors
  1. Hua Ning Liu
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  2. Wen Peng Zhang
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Corresponding author

Correspondence to Hua Ning Liu.

Additional information

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

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Liu, H.N., Zhang, W.P. Mean Value on the Difference Between a Quadratic Residue and Its Inverse Modulo p . Acta Math Sinica 23, 915–924 (2007). https://doi.org/10.1007/s10114-005-0847-3

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  • DOI: https://doi.org/10.1007/s10114-005-0847-3

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