Results 11 to 20 of about 193 (46)

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

On the generalized exponential sums and their fourth power mean

Open Mathematics
The main purpose of this article is to study the calculating problem of the fourth power mean of the two-term exponential sums and provide an accurate calculating formula for utilizing analytical methods and character sums’ properties. In the meantime, a
Liu Wencong, Ning Shushu
doaj   +1 more source

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

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  

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  

On the logarithmic factor in error term estimates in certain additive congruence problems

, 2005
We remove logarithmic factors in error term estimates in asymptotic formulas for the number of solutions of a class of additive congruences modulo a prime number.Comment: 13 ...
Garaev, M. Z.
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 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

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

Miniscule representations, Gauss sum and modular invariance [PDF]

, 2007
After explaining the concepts of Langlands dual and miniscule representations, we define an analog of the Gauss sum for any compact, simple Lie group with a simply laced Lie algebra.
Wu, Siye
core   +1 more source