• Mean Value Estimates of the Error Terms of Lehmer Problem

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      https://www.ias.ac.in/article/fulltext/pmsc/120/04/0507-0513

    • Keywords

       

      Lehmer problem; Kloosterman sum; Gauss sum.

    • 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 $bc\equiv a(\mathrm{mod} p),1\leq b, c < p$ and with $b, c$ having different parity. The main purpose of this paper is to study the mean square value problem of $N(a,p)-\frac{1}{2}(p-1)$ over interval $(N, N+M]$ with $M,N$ positive integers by using the analytic methods, and finally by obtaining a sharp asymptotic formula.

    • Author Affiliations

       

      Dongmei Ren1 Yaming Lu2

      1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China
      2. Research Center for Basic Science, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, People’s Republic of China
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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