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Start Over Subject hybrid mean value

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. 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

4. On Lehmer's problem and Dedekind sums

Creator:
Pan, Xiaowei and Zhang, Wenpeng
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Lehmer's problem, error term, Dedekind sums, hybrid mean value, and asymptotic formula
Language:
English
Description:
Let $p$ be an odd prime and $c$ a fixed integer with $(c, p)=1$. For each integer $a$ with $1\le a \leq p-1$, it is clear that there exists one and only one $b$ with $0\leq b \leq p-1$ such that $ab \equiv c $ (mod $p$). Let $N(c, p)$ denote the number of all solutions of the congruence equation $ab \equiv c$ (mod $p$) for $1 \le a$, $b \leq p-1$ in which $a$ and $\overline {b}$ are of opposite parity, where $\overline {b}$ is defined by the congruence equation $b\overline {b}\equiv 1\pmod p$. The main purpose of this paper is to use the properties of Dedekind sums and the mean value theorem for Dirichlet $L$-functions to study the hybrid mean value problem involving $N(c,p)-\frac {1}{2}\phi (p)$ and the Dedekind sums $S(c,p)$, and to establish a sharp asymptotic formula for it.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public