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1. A hybrid mean value related to certain Hardy sums and Kloosterman sums

Creator:
Guo, Xiaoyan and Zhang, Wenpeng
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Hardy sums, the Kloosterman sums, hybrid mean value, asymptotic formula, and identity
Language:
English
Description:
The main purpose of this paper is using the mean value formula of Dirichlet L-functions and the analytic methods to study a hybrid mean value problem related to certain Hardy sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On the mean value of Dedekind sum weighted by the quadratic Gauss sum

Creator:
Wang, Tingting and Zhang, Wenpeng
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Dedekind sum, quadratic Gauss sum, mean value, and identity
Language:
English
Description:
Various properties of classical Dedekind sums $S(h, q)$ have been investigated by many authors. For example, Wenpeng Zhang, On the mean values of Dedekind sums, J. Théor. Nombres Bordx, 8 (1996), 429–442, studied the asymptotic behavior of the mean value of Dedekind sums, and H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs No. 16, The Mathematical Association of America, Washington, D.C., 1972, studied the related properties. In this paper, we use the algebraic method to study the computational problem of one kind of mean value involving the classical Dedekind sum and the quadratic Gauss sum, and give several exact computational formulae for it.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. 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