A Note on a Kind of Character Sums over the Short Interval

Proceedings Mathematical Sciences

Yulong Zhang¹  Rong Ma² 

[1] The School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 00, People’s Republic of China$$;School of Science, Northwestern Polytechnical University, Xi’an, Shaanxi 00, People’s Republic of China$$

关键词: Character sum;    short interval;    inverse of integers;    estimate.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let 𝑝 be a prime, 𝜒 denote the Dirichlet character modulo 𝑝 and $L(p)={ainmathbb{Z}^+|(a,p)=1,aā≡ 1(mathrm{mod} p),|a - ā|≤ H}$. We study the distribution of elements in the set $L(p)$ in character over the short interval. In this paper, we use the analytic method and show the distribution property ofegin{equation*}sum_{substack{n≤ N}{nin L(p)}}𝜒(n),end{equation*}and give a non-trivial estimate.

【 授权许可】

Unknown