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| ON THE GENERALIZED GLAISHER-HONG'S CONGRUENCES |
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Citation： |
I. SLAVUTSKII.ON THE GENERALIZED GLAISHER-HONG'S CONGRUENCES[J].Chinese Annals of Mathematics B,2002,23(1):63~66 |
| Page view： 1322
Net amount： 935 |
Authors： |
I. SLAVUTSKII; |
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| Abstract： |
Recently Hong Shaofang$^{[6]}$ has investigated the sums $\sum_{j=1}^{p-1}\limits (np+j)^{{-r}}$ (with an odd prime number $p\geq 5$ and $n , r \in {\bold N}$) 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 $\sum_{j=1}^{p^{l}-1}\limits {(np^{l}+j)}^{{-r}},l \in {\bold N}$, may be studied by elementary methods. |
Keywords： |
Glaisher’s congruence, kth Bernoulli number, Kummer-Staudt’s congruence, p-adic L-function |
Classification： |
11A07, 11A41, 11B68, 11S80 |
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