• Mean Value Estimates of the Error Terms of Lehmer Problem

• # Fulltext

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 $bc\equiv a(\mathrm{mod} p),1\leq b, c &lt; p$ 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

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

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019