Czechoslovak Mathematical Journal, Vol. 63, No. 1, pp. 281-288, 2013

Two identities related to Dirichlet character of polynomials

Weili Yao, Wenpeng Zhang

Weili Yao (corresponding author), Department of Mathematics, College of Sciences, Shanghai University, Shanghai, P. R. China, e-mail:; Wenpeng Zhang, Department of Mathematics, Northwest University, Xi'an, Shaanxi, P. R. China, e-mail:

Abstract: Let $q$ be a positive integer, $\chi$ denote any Dirichlet character $\mod q$. For any integer $m$ with $(m, q)=1$, we define a sum $C(\chi, k, m; q)$ analogous to high-dimensional Kloosterman sums as follows:
C(\chi, k, m; q)=\sumprime_{a_1=1}^q \sumprime_{a_2=1}^q \cdots\sumprime_{a_k=1}^q \chi(a_1+a_2+\cdots+a_k+m\overline{a_1a_2\cdots a_k}),
where $a\cdot\overline{a}\equiv1\bmod q$. The main purpose of this paper is to use elementary methods and properties of Gauss sums to study the computational problem of the absolute value $|C(\chi, k, m; q)|$, and give two interesting identities for it.

Keywords: Dirichlet character of polynomials, sum analogous to Kloosterman sum, identity, Gauss sum

Classification (MSC 2010): 11L05

Full text available as PDF.

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at
Subscribers of Springer need to access the articles on their site, which is

[Previous Article] [Contents of This Number] [Contents of Czechoslovak Mathematical Journal]