| ON THE GENERALIZED GLAISHER－HONG‘S CONGRUENCES |
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| 引用本文： | I. SLAVUTSKII. ON THE GENERALIZED GLAISHER－HONG‘S CONGRUENCES[J]. 数学年刊B辑(英文版), 2002, 23(1): 63-66 |
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| 作者姓名： | I. SLAVUTSKII |
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| 作者单位： | I. SLAVUTSKII str. Hamarva,4,O.Box 23393,Akko,Israel. E-mail: nickl@bezeqint.net |
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| 摘 要： | 51. Notations and IntroductionListed below are some general notations which wi1l be used thIoughout this note:pea prime number greater than 3,cl l, mt r, s E N,(:) = n!/(kl(n -- k)!)--the binomial coefficient,Bk--the kth Bernoulli number in the "even suthe" notation, e.g., Bo = 1, B1 =--1/2, B2 = 1/6, B3 = 0,',B.(x) = Z (:)Bkx"--*--the Bernoulli polynomial.k=0As is known, the Bernoulli numbers are defined by the symbolic recurrence relationB.+l = (B + 1)"+', n = 1, 2,', Bo = l, whic…
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| 关 键 词： | 广义Glaisher－Hong同余 素数 Bernoulli数 Kummer－Staudt同余 |
| 收稿时间： | 2000-09-18 |
ON THE GENERALIZED GLAISHER-HONG'S CONGRUENCES |
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| I. SLAVUTSKII. ON THE GENERALIZED GLAISHER-HONG'S CONGRUENCES[J]. Chinese Annals of Mathematics,Series B, 2002, 23(1): 63-66 |
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| Authors: | I. SLAVUTSKII |
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| Affiliation: | str. Hamarva, 4, O.Box 23393, Akko, Israel. |
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| Abstract: | 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. |
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| Keywords: | Glaisher's congruence kth Bernoulli number Kummer-Staudt's congruence p-adic L-function |
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