Results 1 to 10 of about 1,790 (152)

On a Kind of Dirichlet Character Sums [PDF]

Abstract and Applied Analysis, 2013
Let p≥3 be a prime and let χ denote the Dirichlet character modulo p.
Rong Ma, Yulong Zhang, Guohe Zhang
doaj   +3 more sources

Mean values of cubic and quartic Dirichlet characters [PDF]

Functiones Et Approximatio, Commentarii Mathematici, 2020
12 ...
Liangyi Zhao
exaly   +6 more sources

Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8

Open Mathematics
In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
doaj   +2 more sources

Two identities related to dirichlet character of polynomials [PDF]

Czechoslovak Mathematical Journal, 2013
The authors study sums, analogous to Kloosterman sums. They prove two theorems: Theorem 1. Let \(q\) be an odd number, \(\chi \) be a Dirichlet character mod \(q\), \(k\) and \(m\) be positive integers such that \((km,q)=1\) and \((k+1,\varphi (q))=1\). Then for any primitive character \(\chi \bmod q\), we have the identity \[ | C(\chi ,k,m;q)| = \left|
Weili Yao, Zhang Wenpeng, Yao Weili
exaly   +3 more sources

A note on the Dirichlet characters of polynomials

Mathematica Slovaca, 2014
Abstract The main purpose of this paper is using the analytic methods and the properties of character sums to study the computational problem of several kind character sums of polynomials mod q, an odd square-full number, and give two interesting identities for them.
Wenpeng Zhang, Tingting Wang
exaly   +2 more sources

Dirichlet expression for L(1, χ) with general Dirichlet character

Proceedings of the Indian Academy of Sciences: Mathematical Sciences, 2010
In the famous work of Dirichlet on class number formula, L(s, χ) at s = 1 has been expressed as a finite sum, where L(s, χ) is the Dirichlet L-series of a real Dirichlet character. We show that this expression with obvious modification is valid for the general primitive Dirichlet character χ.
exaly   +2 more sources

Multiple Lucas–Dirichlet Series Associated With Additive and Dirichlet Characters [PDF]

Mediterranean Journal of Mathematics, 2021
20 ...
N. K. Meher, S. S. Rout
openaire   +3 more sources

Exceptional characters and nonvanishing of Dirichlet L-functions [PDF]

Mathematische Annalen, 2021
Let $ψ$ be a real primitive character modulo $D$. If the $L$-function $L(s,ψ)$ has a real zero close to $s=1$, known as a Landau-Siegel zero, then we say the character $ψ$ is exceptional. Under the hypothesis that such exceptional characters exist, we prove that at least fifty percent of the central values $L(1/2,χ)$ of the Dirichlet $L$-functions $L(s,
Hung M. Bui, Kyle Pratt, Alexandru Zaharescu   +2 more
openaire   +2 more sources

A Bound for a Sum of Products of Two Characters and Its Application

Mathematics, 2023
Using the exponent pair method, a bound is derived for the sum ∑manb≤xχ1a(m)χ2b(n), where a,b are fixed positive integers, χ1,χ2 are primitive Dirichlet characters modulo q1 and q2, respectively, and χ1a,χ2b are not principal characters.
Teerapat Srichan
doaj   +1 more source

A Certain Mean Square Value Involving Dirichlet L-Functions

Mathematics, 2020
The main purpose of this article is using the elementary methods, the properties of Dirichlet L-functions to study the computational problem of a certain mean square value involving Dirichlet L-functions at positive integer points, and give some exact ...
Wenpeng Zhang, Di Han
doaj   +1 more source