منابع مشابه
Congruences 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...
متن کاملIdentities of Bernoulli Numbers and Polynomials
In the field of Laurent series Q((T)), the series B = T/(e T − 1) is contained in the formal power series ring Q[[T ]]. The i-th Bernoulli number B
متن کاملGeneralizations of Bernoulli Numbers and Polynomials
The concepts of Bernoulli numbers B n , Bernoulli polynomials B n (x), and the generalized Bernoulli numbers B n (a, b) are generalized to the one B n (x; a, b, c) which is called the generalized Bernoulli polynomials depending on three positive real parameters. Numerous properties of these polynomials and some relationships between B n , B n (x), B n (a, b), and B n (x; a, b, c) are established.
متن کاملNumerical Semigroups, Cyclotomic Polynomials, and Bernoulli Numbers
We give two proofs of a folkore result relating numerical semigroups of embedding dimension two and binary cyclotomic polynomials and explore some consequences. In particular, we give a more conceptual reproof of a result of Hong et al. (2012) on gaps between the exponents of non-zero monomials in a binary cyclotomic polynomial. The intent of the author with this paper is to popularise cyclotom...
متن کاملIdentities on The Bernoulli and Genocchi Numbers and Polynomials
Let p be a fixed odd prime number. Throughout this paper Zp,Qp, and Cp will denote the ring of p-adic rational integers, the field of p-adic rational numbers, and the completion of the algebraic closure of Qp. Let N be the set of natural numbers and Z N ∪ {0}. The p-adic norm on Cp is normalized so that |p|p p−1. Let C Zp be the space of continuous functions on Zp. For f ∈ C Zp , the fermionic ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2015
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2015.05.019