Two identities related to Dirichlet character of polynomials

Yao, Weili, and Zhang, Wenpeng. "Two identities related to Dirichlet character of polynomials." Czechoslovak Mathematical Journal 63.1 (2013): 281-288. <http://eudml.org/doc/252470>.

@article{Yao2013,
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: \[ C(\chi , k, m; q)=\sum \_\{a\_1=1\}^\{q\}\{\}^\{\prime \} \sum \_\{a\_2=1\}^\{q\}\{\}^\{\prime \} \cdots \sum \_\{a\_k=1\}^\{q\}\{\}^\{\prime \} \chi (a\_1+a\_2+\cdots +a\_k+m\overline\{a\_1a\_2\cdots a\_k\}), \] where $a\cdot \overline\{a\}\equiv 1\;\@mod \;q$. 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.},
author = {Yao, Weili, Zhang, Wenpeng},
journal = {Czechoslovak Mathematical Journal},
keywords = {Dirichlet character of polynomials; sum analogous to Kloosterman sum; identity; Gauss sum; primitive character; Gauss sum; Kloosterman sum},
language = {eng},
number = {1},
pages = {281-288},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Two identities related to Dirichlet character of polynomials},
url = {http://eudml.org/doc/252470},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Yao, Weili
AU - Zhang, Wenpeng
TI - Two identities related to Dirichlet character of polynomials
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 281
EP - 288
AB - 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: \[ C(\chi , k, m; q)=\sum _{a_1=1}^{q}{}^{\prime } \sum _{a_2=1}^{q}{}^{\prime } \cdots \sum _{a_k=1}^{q}{}^{\prime } \chi (a_1+a_2+\cdots +a_k+m\overline{a_1a_2\cdots a_k}), \] where $a\cdot \overline{a}\equiv 1\;\@mod \;q$. 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.
LA - eng
KW - Dirichlet character of polynomials; sum analogous to Kloosterman sum; identity; Gauss sum; primitive character; Gauss sum; Kloosterman sum
UR - http://eudml.org/doc/252470
ER -