Results 11 to 20 of about 174 (27)

Abel Summation of Ramanujan-Fourier Series [PDF]

, 2015
Using Abel summation the paper proves a weak form of the Wiener-Khinchin formula for arithmetic functions with point-wise convergent Ramanujan-Fourier expansions.
Washburn, John
core  

A Conversion Formula for One Kind Fourth Power Mean of Kloosterman Sums and the Character Sums Module p

Journal of Mathematics, Volume 2024, Issue 1, 2024.
The primary contribution of this paper is to research one kind special Kloosterman sums using analytic method. We translate one kind fourth power mean of the Kloosterman sums into the character sums of one kind polynomials. It is possible to construct an exact formula for the fourth power mean of one kind Kloosterman sums by computing the character ...
Shushu Ning, Xuexia Wang, Ming-Sheng Liu
wiley   +1 more source

On the non-vanishing of certain Dirichlet series

, 2017
Given $k\in\mathbb N$, we study the vanishing of the Dirichlet series $$D_k(s,f):=\sum_{n\geq1} d_k(n)f(n)n^{-s}$$ at the point $s=1$, where $f$ is a periodic function modulo a prime $p$.
Bettin, Sandro, Martin, Bruno
core   +2 more sources

A study on two types of degenerate unipoly-Dedekind sums

Applied Mathematics in Science and Engineering
In this paper, we study the degenerate unipoly-Dedekind sums rising from the type 2 degenerate unipoly Bernoulli functions and degenerate unipoly-Bernoulli functions of arbitrary indices, respectively.
Wencong Liu, Lingling Luo, Hye Kyung Kim, Taekyun Kim   +3 more
doaj   +1 more source

On the number of solutions of a restricted linear congruence

, 2017
Consider the linear congruence equation $${a_1^{s}x_1+\ldots+a_k^{s} x_k \equiv b\,(\text{mod } n^s)}\text { where } a_i,b\in\mathbb{Z},s\in\mathbb{N}$$ Denote by $(a,b)_s$ the largest $l^s\in\mathbb{N}$ which divides $a$ and $b$ simultaneously.
Namboothiri, K Vishnu
core   +1 more source

Evaluating Binomial Character Sums Modulo Powers of Two [PDF]

, 2014
We show that for any mod $2^m$ characters, $\chi_1, \chi_2,$ the complete exponential sum, $$ \sum_{x=1}^{2^m}\chi_1(x) \chi_2(Ax^k+B), $$ has a simple explicit ...
Pigno, Vincent, Pinner, Chris, Sheppard, Joe   +2 more
core  

From a cotangent sum to a generalized totient function

, 2017
In this paper we investigate a certain category of cotangent sums and more specifically the sum $$\sum_{m=1}^{b-1}\cot\left(\frac{\pi m}{b}\right)\sin^{3}\left(2\pi m\frac{a}{b}\right)\:$$ and associate the distribution of its values to a generalized ...
Rassias, Michael Th.
core   +1 more source

Moments of averages of generalized Ramanujan sums

, 2015
Let $\beta$ be a positive integer. A generalization of the Ramanujan sum due to Cohen is given by \begin{align} c_{q,\beta }(n) := \sum\limits_{{{(h,{q^\beta })}_\beta } = 1} {{e^{2\pi inh/{q^\beta }}}}, \nonumber \end{align} where $h$ ranges over the ...
Robles, Nicolas, Roy, Arindam
core   +1 more source

One special kind of Kloosterman sum and its fourth-power mean

Open Mathematics
This article aims to investigate the calculation problem of the fourth-power mean of the specific Kloosterman sums by utilizing analytic methods and the properties of classical Gauss sums.
Zhang Wenpeng, Wang Li, Liu Xiaoge
doaj   +1 more source

Generalized quadratic Gauss sums and their 2mth power mean

Open Mathematics
The main purpose of this article is to study the problem of calculating the 2mth power mean of the generalized quadratic Gauss sums, and using the analytic method and an interesting combinatorial identity to give a sharp asymptotic formula for the 2mth ...
Cui Dewang, Zhang Wenpeng
doaj   +1 more source