ON THE GENERALIZED GLAISHER-HONG'S CONGRUENCES
被引量：1
ON THE GENERALIZED GLAISHER-HONG'S CONGRUENCES
摘要
Recently Hong Shaofang[6] has investigated the sums (np + j)-r ( with an odd prime number p 5 and n, r N) by Washington’s p-adic expansion of these sums as a power series in n where the coefficients are values of p-adic L-fuctions[12]. Herethe author shows how a more general sums (npl +j)-r,l N, may be studied by elementary methods.
二级参考文献9
-
1[1]Boyd, D., A p-adic study of the partial sums of the harmonic series, Experiment Math.[2](1994),[2]87-302.
-
2[2]Dickson, L. E., History of the Theory of Numbers, Vol. I, Chelsea, New York, 1952 (especially Chapter[2]).
-
3[3]Glaisher, J. W. L., On the residues of the sums of products of the first p-1 numbers,and their powers,to modulus p2 or pa, Quart. J. Pure Appl. Math.,[2]1(1900),321-353.
-
4[4]Glaisher, J. W. L., On the residues of the inverse powers of numbers in arithmetic progression, Quart.J. Pure Appl. Math.,[2]2(1901),[2]71-305.
-
5[5]Hardy, G. H. & Wright, E. M., An Introduction to the Theory of Numbers,[4]th ed. Oxford Univ. Press,London, 1960.
-
6[6]Ireland, K. & Rosen, M., A Classical Introduction to Modern Number Theory, Springer-Verlag, New York, 1982.
-
7[7]Lehmer, E., On congruences involving Bernoulli numbers and the quotients of Fermat and Wilson, Ann.Math.,[2]9(1938),[2]50-360.
-
8[8]Washington, L., p-adic L-functions and sums of powers, J. Number Theory,[6]9(1998),[5]0-61.
-
9[9]Washington, L., Introduction to Cyclotomic Fields, Springer-Verlag, New York, 1982.
-
1HONGSHAOFANG.NOTES ON GLAISHER'S CONGRUENCES[J].Chinese Annals of Mathematics,Series B,2000,21(1):33-38. 被引量：3
-
2An Elementary Method on a Minimization Problem[J].数学理论与应用,2000,20(4):83-84.
-
3Qing Lin LU Zheng Ke MIAO.Congruences for a Restricted m-ary Overpartition Function[J].Journal of Mathematical Research and Exposition,2010,30(5):939-943.
-
4CHENG Zi-qiang ZHOU Yuan-lan PAN Shi-ju.Rectangular Ring Congruences on an E-inversive Semiring[J].Chinese Quarterly Journal of Mathematics,2014,29(4):529-538.
-
5Refik KESKIN DEMiRTURK BITIM.Fibonacci and Lucas Congruences and Their Applications[J].Acta Mathematica Sinica,English Series,2011,27(4):725-736.
-
6Todd Cochrane (Department of Mathematics,Kansas State University,Manhattan,KS 66506.U.S.A)(Email:cochrane@math.ksu.edu)Zheng Zhiyong (Department of Mathematics,Zhongshan University,Guangzhou 510275,China)(Email:addsr03@zsulink.zsu.edu.en).Small Solutions of the Congruence a_1x_1~2+a_2x_2~2+a_3x_3~2+a_4x_4~2≡c(mod p)[J].Acta Mathematica Sinica,English Series,1998,14(2):175-182.
-
7Jiangping XIAO,Yonghua LI.Congruences on Zappa-Szp Products of Semilattices with An Identity and Groups[J].Journal of Mathematical Research with Applications,2012,32(6):677-686.
-
8康金玉.英国国家物理研究所信息技术[J].技术监督参考,1989(9):24-27.
-
9张伟平.COBORDISM AND ROKHLIN CONGRUENCES[J].Acta Mathematica Scientia,2009,29(3):609-612.
-
10ZHANG Yong,PAN Hao.Some 3-adic congruences for binomial sums[J].Science China Mathematics,2014,57(4):711-718. 被引量：1
