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2-Adic Congruences of Nörlund Numbers and of Bernoulli Numbers of the Second Kind

✍ Scribed by Arnold Adelberg

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
233 KB
Volume
73
Category
Article
ISSN
0022-314X

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✦ Synopsis

In this paper, we find simple 2-adic congruences mod 2 [nÂ2]+1 for the No rlund numbers B (n) n and for the Bernoulli numbers of the second kind b n . These congruences improve F. T. Howard's mod 8 congruences (in ``Applications of Fibonacci Numbers, '' Vol. 5, pp. 355 366, Kluwer Academic, Dordrecht, 1993). We use recurrence relations to determine when our congruences are best possible and to obtain further information about the 2-adic expansions of B (n) n Ân ! and of b n .

1998 Academic Press

These expansions should be considered as formal power series (although (1) converges in the complex domain if |t| <2?, while (2) and (3) converge if |t| <1), since a feature of our approach is the interplay between formal and 2-adic convergent power series.

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