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- W2799236807 abstract "In this paper, we use our previous study of the higher order Bernoulli numbers $B_n^{(l)}$ to investigate the $p$-adic properties of the Stirling numbers of the second kind $S(n,k)$. For example, we give a new, greatly simplified proof of the formula $nu_2(S(2^h,k))=d_2(k)-1$ if $1le k le 2^h$, and generalize this result to arbitrary primes $p$. We also consider the Stirling numbers of the first kind $s(n,k)$, with new results analogous to those for the Stirling numbers of the second kind. New mod $p$ congruences for Stirling numbers of both kinds are also given." @default.
- W2799236807 created "2018-05-07" @default.
- W2799236807 creator A5005489838 @default.
- W2799236807 date "2018-05-02" @default.
- W2799236807 modified "2023-09-27" @default.
- W2799236807 title "The $p$-adic Analysis of Stirling Numbers via Higher Order Bernoulli Numbers" @default.
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