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On the Residues of binomial coefficients and Their Products Modulo Prime Powers

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Acta Mathematica Sinica,English Series 2002年第2期18卷 277-288页

作者： CAI Tian Xin Department of Mathematics.Zhejiang University.Hangzhou 310028,P.R.China E-mail:trcai@mail.hz.zj.cnGRANVILLE Andrew Department of Mathematics,University of Georgia.Athens,GA 30602.USA E-mail:andrew@sophie.math.uga.edu Department of Mathematics Zhejiang University Hangzhou P. R. China Department of Mathematics University of Georgia Athens USA

In this paper,we show several arithmetic properties on the residues of binomial coefficients and their products modulo prime powers,e.g.. for any distinct odd primes p and q.Meanwhile.we discuss the connections with ... 详细信息

关键词： binomial coefficients Bernoulli numbers Recognizing primes

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On a Supercongruence Conjecture of Z.-W.Sun

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Chinese Annals of Mathematics,Series B 2022年第3期43卷 417-424页

作者： Guo-shuai MAO Department of Mathematics Nanjing University of Information Science and TechnologyNanjing 210044China

In this paper,the author partly proves a supercongruence conjectured by Z.-W.Sun in 2013.Let p be an odd prime and let a∈Z^(+).Then,if p≡1(mod 3),[5/6p^(a)]∑k=0(2kk)/16^(k)≡(3/p^(a))(mod p^(2))is obtained,where(■... 详细信息

关键词： Supercongruences binomial coefficients Fermat quotient Jacobi symbol

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Analytical evaluation of the plasma dispersion function for a Fermi-Dirac distribution

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Chinese Physics B 2012年第5期21卷 400-404页

作者： B.A.Mamedov Department of Physics Faculty of Arts and SciencesGaziosmanpa sa University

An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed.The new method has been developed using the binomial expansion theorem and the Gamma functions.The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function.The resulting series present better convergence rates.Several acceleration techniques are combined to further improve the efficiency.The obtained results for the plasma dispersion function are in good agreement with the known numerical data.

关键词： Fermi Dirac distribution plasma dispersion function binomial coefficients incompletegamma functions

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N-Summet-k and Its Application in the Construction of Pascal Triangle and Pascal Matrix

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Journal of Applied Mathematics and Physics 2016年第1期4卷 169-177页

作者： Neelam Jeevan Kumar Department of Electrical and Electronics Engineering Jawaharlal Nehru Technological University Hyderabad College of Engineering Jagtial India

Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal triangle elements and pascal matrix formation, etc. This paper explains about its functions and properties of N-Summet-k. The result of variation between N and k is shown in tabulation.

关键词： Summetor N-Summet-k binomial coefficients Pascal’s Triangle Pascal’s Matrix