Results 31 to 40 of about 2,373,714 (282)
On the fourth power mean of the general Kloosterman sums
Journal of Number Theory, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wenpeng Zhang
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A sum analogous to Kloosterman sum and its fourth power mean
AIMS Mathematics, 2020 The main purpose of this paper is using the analytic methods and the properties of the Legendre’s symbol and quadratic residue mod p to study the computational problem of the fourth power mean of a sum analogous to Kloosterman sum, and give a sharp ...
He Yan-qin, Zhu Chaoxi, Chen Zhuo-yu
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ON THE FOURTH POWER MEAN OF GENERALIZED TWO-TERM EXPONENTIAL SUMS [PDF]
Bulletin of the Korean Mathematical Society, 2013 In this paper, we use the elementary method and the theory of complex functions to study the computational problem of the fourth power mean of the generalized two-term exponential sums, and give two exact identities for them.
Tingting Wang
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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\
Wenpeng Zhang, Shimeng Shen
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Retracted Article: On the fourth power mean of the two-term exponential sums [PDF]
Journal of Inequalities and Applications, 2014 AbstractThe 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 ...
Minhui Zhu, Di Han
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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 \(\mod{q}\).
Hui Chen, Tianping Zhang
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The fourth and sixth power mean of the classical Kloosterman sums
Journal of Number Theory, 2011 Let \(S(m,n;q)\) be the classical Kloosterman sums and \(q\geq 3\). The paper obtains: For \((n,q)=1\), then \[ \sum\limits_{m=1}^{q}|S(m,n;q)|^{4}=3^{\omega(q)}q^{2}\varphi(q)\prod\limits_{p\|q}\left(\frac{2}{3}-\frac{1}{3p}-\frac{4}{3p(p-1)}\right), \] where \(\omega(q)\) denotes the number of all different prime divisors of \(q\) and \(\varphi(q ...
openaire +3 more sources
Power System Parameters Forecasting Using Hilbert-Huang Transform and Machine Learning [PDF]
Известия Иркутского государственного университета: Серия "Математика", 2014 A novel hybrid data-driven approach is developed for forecasting power system parameters with the goal of increasing the efficiency of short-term forecasting studies for non-stationary time-series. The proposed approach is based on mode decomposition and
V.G. Kurbatsky +5 more
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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
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e-Prime: Advances in Electrical Engineering, Electronics and Energy, 2021 This research uses computational fluid dynamics (CFD) to perform a two-stage optimization of power output in multiple vertical-axis wind turbines (VAWT) with straight blades.
Wei-Hsin Chen +6 more
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