## Abstract and Applied Analysis

### On a Kind of Dirichlet Character Sums

#### Abstract

Let $p\ge \mathrm{3}$ be a prime and let $\chi$ denote the Dirichlet character modulo $p$. For any prime $q$ with $q, define the set $E(q,p)=\{a\mid 1\le a,\stackrel{-}{a}\le p,a\stackrel{-}{a}\equiv 1(\text{mod}p)\text{\hspace\{0.17em\}\hspace\{0.17em\}and\hspace\{0.17em\}\hspace\{0.17em\}}a\equiv \stackrel{-}{a}(\text{mod}q)\}$. In this paper, we study a kind of mean value of Dirichlet character sums $\sum a\le p\mathrm{ a}\in E(q,p)\chi (a)$, and use the properties of the Dirichlet $L$-functions and generalized Kloosterman sums to obtain an interesting estimate.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 750964, 8 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393448833

Digital Object Identifier
doi:10.1155/2013/750964

Mathematical Reviews number (MathSciNet)
MR3102680

Zentralblatt MATH identifier
07095326

#### Citation

Ma, Rong; Zhang, Yulong; Zhang, Guohe. On a Kind of Dirichlet Character Sums. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 750964, 8 pages. doi:10.1155/2013/750964. https://projecteuclid.org/euclid.aaa/1393448833

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