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Start Over Subject Dedekind sums

1. A hybrid mean value of the Dedekind sums

Creator:
Yang, Hai
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Dedekind sums, Dirichlet $L$-function, and mean value
Language:
English
Description:
The main purpose of this paper is to use the M. Toyoizumi's important work, the properties of the Dedekind sums and the estimates for character sums to study a hybrid mean value of the Dedekind sums, and give a sharper asymptotic formula for it.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. 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

3. On the k-polygonal numbers and the mean value of Dedekind sums

Creator:
Guo, Jing and Li, Xiaoxue
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, hodnoty, Dedekindovy okruhy, mathematics, values, Dedekind rings, Dedekind sums, mean value, computational problem, k-polygonal number, analytic method, 13, and 51
Language:
English
Description:
For any positive integer k ≥ 3, it is easy to prove that the k-polygonal numbers are an(k) = (2n+n(n−1)(k−2))/2. The main purpose of this paper is, using the properties of Gauss sums and Dedekind sums, the mean square value theorem of Dirichlet L-functions and the analytic methods, to study the computational problem of one kind mean value of Dedekind sums S(an(k)ām(k), p) for k-polygonal numbers with 1 ≤ m, n ≤ p − 1, and give an interesting computational formula for it., Jing Guo, Xiaoxue Li., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public