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Mean value estimates of the error terms of Lehmer problem

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Abstract

Let p be an odd prime and a be an integer coprime with p. Denote by N(a, p) the number of pairs of integers b, c with bc ≡ a(mod p), 1 ≤ b, c < p and with b, c having different parity. The main purpose of this paper is to study the mean square value problem of (N(a, p) − 1/2 (p−1)) over interval (N, N + M] with M, N positive integers by using the analytic methods, and finally by obtaining a sharp asymptotic formula.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Dongmei Ren

  2. Research Center for Basic Science, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, People’s Republic of China

    Yaming Lu

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  1. Dongmei Ren
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  2. Yaming Lu
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Correspondence to Dongmei Ren.

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Ren, D., Lu, Y. Mean value estimates of the error terms of Lehmer problem. Proc Math Sci 120, 507–513 (2010). https://doi.org/10.1007/s12044-010-0042-z

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  • DOI: https://doi.org/10.1007/s12044-010-0042-z

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