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Start Over Subject Dirichlet character of polynomials

1. A hybrid mean value involving two-term exponential sums and polynomial character sums

Creator:
Di, Han
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Dirichlet character of polynomials, two-term exponential sums, hybrid mean value, and asymptotic formula
Language:
English
Description:
Let $q \ge 3$ be a positive integer. For any integers $m$ and $n$, the two-term exponential sum $C(m,n,k;q)$ is defined by $C(m,n,k;q) = \sum _{a=1}^q e ({(ma^k +na)}/{q})$, where $e(y)={\rm e}^{2\pi {\rm i} y}$. In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Two identities related to Dirichlet character of polynomials

Creator:
Yao, Weili and Zhang, Wenpeng
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Dirichlet character of polynomials, sum analogous to Kloosterman sum, identity, and Gauss sum
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public