✦ LIBER ✦

Congruences ofp-adic Integer Order Bernoulli Numbers

✍ Scribed by Arnold Adelberg

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 483 KB
Volume: 59
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0103

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we establish some new congruences of p-adic integer order Bernoulli numbers. These generalize the Kummer congruences for ordinary Bernoulli numbers. We apply our congruences to prove irreducibility of certain Bernoulli polynomials with order divisible by p and to get new congruences for Stirling numbers.

📜 SIMILAR VOLUMES

p-adic Proofs of congruences for the Ber

p-adic Proofs of congruences for the Bernoulli numbers

✍ Wells Johnson 📂 Article 📅 1975 🏛 Elsevier Science 🌐 English ⚖ 655 KB

2-Adic Congruences of Nörlund Numbers an

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

✍ Arnold Adelberg 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 233 KB

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, Dordrech

Universal Higher Order Bernoulli Numbers

Universal Higher Order Bernoulli Numbers and Kummer and Related Congruences

✍ Arnold Adelberg 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 146 KB

We define higher or arbitrary order universal Bernoulli numbers and higher order universal Bernoulli Hurwitz numbers. We deduce a universal first-order Kummer congruence and a congruence for the higher order universal Bernoulli Hurwitz numbers from Clarke's universal von Staudt theorem. We also esta

On the Invariant Factors of Kummer Order

On the Invariant Factors of Kummer Orders in the Rings of Integers of p-adic Number Fields of Degreep2

✍ Yoshimasa Miyata 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 356 KB

Let KÂk be an extension of degree p 2 over a p-adic number field k with the Galois group G. We study the Galois module structure of the ring O K of integers in K. We determine conditions under which the invariant factors of Kummer orders O K t in O K of two extensions coincide with each other and gi