Mean Value Estimates of the Error Terms of Lehmer Problem

Proceedings Mathematical Sciences

Yaming Lu²  Dongmei Ren¹ 

[1] School of Mathematics and Statistics, Southwest University, Chongqing 00, People’s Republic of China$$;Research Center for Basic Science, Xi’an Jiaotong University, Xi’an, Shaanxi 00, People’s Republic of China$$

关键词: Lehmer problem;    Kloosterman sum;    Gauss sum.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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

【 授权许可】

Unknown