Geodesic
Two identities related to Dirichlet character of polynomials
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 281-288.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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: $$ C(\chi, k, m; q)=\sum _{a_1=1}^{q}{}' \sum _{a_2=1}^{q}{}' \cdots \sum _{a_k=1}^{q}{}' \chi (a_1+a_2+\cdots +a_k+m\overline {a_1a_2\cdots a_k}), $$ where $a\cdot \overline {a}\equiv 1\bmod q$. 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.
DOI : 10.1007/s10587-013-0018-0
Classification : 11L05, 11L40
Keywords: Dirichlet character of polynomials; sum analogous to Kloosterman sum; identity; Gauss sum 
@article{10_1007_s10587_013_0018_0,
     author = {Yao, Weili and Zhang, Wenpeng},
     title = {Two identities related to {Dirichlet} character of polynomials},
     journal = {Czechoslovak Mathematical Journal},
     pages = {281--288},
     publisher = {mathdoc},
     volume = {63},
     number = {1},
     year = {2013},
     doi = {10.1007/s10587-013-0018-0},
     mrnumber = {3035511},
     zbl = {1274.11126},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0018-0/}
}
TY  - JOUR
AU  - Yao, Weili
AU  - Zhang, Wenpeng
TI  - Two identities related to Dirichlet character of polynomials
JO  - Czechoslovak Mathematical Journal
PY  - 2013
SP  - 281
EP  - 288
VL  - 63
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0018-0/
DO  - 10.1007/s10587-013-0018-0
LA  - en
ID  - 10_1007_s10587_013_0018_0
ER  - 
%0 Journal Article
%A Yao, Weili
%A Zhang, Wenpeng
%T Two identities related to Dirichlet character of polynomials
%J Czechoslovak Mathematical Journal
%D 2013
%P 281-288
%V 63
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0018-0/
%R 10.1007/s10587-013-0018-0
%G en
%F 10_1007_s10587_013_0018_0
Yao, Weili; Zhang, Wenpeng. Two identities related to Dirichlet character of polynomials. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 281-288. doi : 10.1007/s10587-013-0018-0. http://geodesic.mathdoc.fr/articles/10.1007/s10587-013-0018-0/

Cité par Sources :