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

Authors: Liu, Hua¹; Zhang, Wen²

Source: Acta Mathematica Sinica, Volume 23, Number 5, May 2007 , pp. 915-924(10)

Publisher: Springer

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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.

Keywords: An integer and its inverse; Bernoulli numbers; Cochrane sums; 11A07

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10114-005-0847-3

Affiliations: 1: Email: hnliu@etang.com 2: Email: wpzhang@nwu.edu.cn

Publication date: 2007-05-01