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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In this article we investigate the Bernoulli numbers B̂n associated to the formal group laws whose canonical invariant differentials generate the Lucas sequences {Un} and {Vn}. We give explicit expressions for these numbers and prove analogues of Kummer congruences for them.
متن کاملCongruences concerning Bernoulli numbers and Bernoulli polynomials
Let {Bn(x)} denote Bernoulli polynomials. In this paper we generalize Kummer’s congruences by determining Bk(p−1)+b(x)=(k(p − 1) + b) (modp), where p is an odd prime, x is a p-integral rational number and p − 1 b. As applications we obtain explicit formulae for ∑p−1 x=1 (1=x ) (modp ); ∑(p−1)=2 x=1 (1=x ) (modp ); (p − 1)! (modp ) and Ar(m;p) (modp), where k ∈ {1; 2; : : : ; p− 1} and Ar(m;p) i...
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ژورنال
عنوان ژورنال: Turkish Journal of Analysis and Number Theory
سال: 2014
ISSN: 2333-1100
DOI: 10.12691/tjant-2-1-4