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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
3. A hybrid mean value related to Dedekind sums
- Creator:
- Li, Jianghua and Wenpeng, Zhang
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- the Dedekind sum, hybrid mean value, asymptotic formula, and identity
- Language:
- English
- Description:
- The main purpose of this paper is to study a hybrid mean value problem related to the Dedekind sums by using estimates of character sums and analytic methods.
- 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