منابع مشابه
Generalized Bernoulli-Hurwitz Numbers and The Universal Bernoulli Numbers
The three fundamental properties of the Bernoulli numbers, namely, the theorem of von Staudt-Clausen, von Staudt’s second theorem, and Kummer’s original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients of power series expansion of a higher genus algebraic function with respect to suitable variable. Our generalization strongly ...
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We investigate sums of products of Bernoulli numbers including poly-Bernoulli numbers. A relation among these sums and explicit expressions of sums of two and three products are given. As a corollary, we obtain fractional parts of sums of two and three products for negative indices.
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Nowadays this result plays important roles in many aspects. Recently Sun and Wan investigated Fp(n, r) mod p in [SW2]. In this paper, using p-adic methods we determine (Fp(m, r) − Fp(n, r))/(m − n) modulo p in terms of Bernoulli numbers, where m > 0 is an integer with m 6= n and m ≡ n (mod p(p − 1)). Consequently, Fp(n, r) mod pordp(n)+1 is determined; for example, if n ≡ n∗ (mod p− 1) with 0 <...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 2005
ISSN: 1776-0852
DOI: 10.2991/jnmp.2005.12.4.3