Results 21 to 30 of about 9,452,959 (273)

A note on the fourth power mean of the generalized Kloosterman sums

Journal of Number Theory, 2017
Let \(p\) be an odd prime, and let \(\alpha\geq 2\) be an integer. Let \(\chi\) be any non-primitive character modulo \(p^{\alpha}\) satisfying \(\chi\neq \chi_0\), the principal character. Let \(n\) be an integer with \((n, p)=1\). This paper proves that \[ \mathop{\sum_{m=1}^{p^{\alpha}}}_{(m,p)=1}\left|\sum_{a=1}^{p^{\alpha}}\chi(a)e\left(\frac{ma+n\
Zhang, Wenpeng, Shen, Shimeng
openaire   +3 more sources

Power Quality Enhancement using Integrated Control Technique Quantum Calculus-based Least Mean Fourth and Optimized Fractional Order Proportional-Integral-Derivative

Electrica
This article proposes the effectiveness of a Dynamic Voltage Restorer (DVR) based on Quantum Calculus-based Least Mean Fourth (q-LMF) for compensating the impact of grid voltage perturbation.
Prashant Kumar, Sabha Raj Arya
doaj   +2 more sources

Retracted Article: On the fourth power mean of the two-term exponential sums [PDF]

Journal of Inequalities and Applications, 2014
Abstract Abstract The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind of fourth power mean of two-term exponential sums, and to give an interesting identity and asymptotic formula for it.
Zhu, Minhui, Han, Di
openaire   +3 more sources

A certain new Gauss sum and its fourth power mean

AIMS Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yan Zhao, Wenpeng Zhang, Xingxing Lv
openaire   +4 more sources

A sum analogous to Kloosterman sum and its fourth power mean

AIMS Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
He Yanqin, Zhu Chaoxi, Chen Zhuoyu
openaire   +4 more sources

On the fourth power mean of the analogous general Kloosterman sum

Journal of Number Theory, 2016
The authors study generalized Kloosterman sums \[ C(m,n,k,\chi;q)= \sum_{a=1}^{q}\chi(a)e\left(\frac{m\bar a^k+na}{q }\right), \] where \(q\), \(m\), \(n\), \(k\) are given positive integers, \(q \geq 3\), \(e(x)=e^{2\pi i x}\), \(a\bar a\equiv 1\pmod{q}\) and \(\chi\) is a character \(\mod{q}\).
Chen, Hui, Zhang, Tianping
openaire   +3 more sources

An explicit formula for the fourth power mean of the Riemann zeta-function

Acta Mathematica, 1993
In this important paper the author establishes an explicit formula for \[ I(T,\Delta)= (\Delta\sqrt{\pi})^{-1} \int_{-\infty}^ \infty |\zeta ({\textstyle {1\over 2}}+iT+it)|^ 4 e^{-(t/\Delta)^ 2} dt \qquad ...
Y. Motohashi
openaire   +3 more sources

The fourth power mean of the generalized two-term exponential sums and its upper and lower bound estimates

Journal of Inequalities and Applications, 2013
In this paper, we use the analytic method and the properties of Gauss sums to study the computational problem of one kind fourth power mean of the generalized two-term exponential sums, and give an exact computational formula for it.MSC:11L40, 11F20.
Xiao-Xue Li, Zhe-Feng Xu
exaly   +2 more sources

On the general Gauss sums and their fourth power mean

Osaka Journal of Mathematics, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wenpeng, Zhang, Huaning, Liu
openaire   +5 more sources

On the fourth power mean of one special two-term exponential sums

AIMS Mathematics, 2023
The main purpose of this paper is using the elementary methods and the number of the solutions of some congruence equations to study the calculating problem of the fourth power mean of one special two-term exponential sums, and give an exact calculating ...
Wen-Peng Zhang, Yuan-Yuan Meng
semanticscholar   +1 more source