共查询到20条相似文献,搜索用时 10 毫秒
1.
Zhi-Hong Sun 《Journal of Number Theory》2008,128(2):280-312
Let [x] be the integral part of x. Let p>5 be a prime. In the paper we mainly determine , , and in terms of Euler and Bernoulli numbers. For example, we have
2.
Hao Pan 《Journal of Combinatorial Theory, Series A》2006,113(1):156-175
Using the finite difference calculus and differentiation, we obtain several new identities for Bernoulli and Euler polynomials; some extend Miki's and Matiyasevich's identities, while others generalize a symmetric relation observed by Woodcock and some results due to Sun. 相似文献
3.
Arnold Adelberg 《Journal of Number Theory》2004,109(2):362-378
We have previously proved Kummer congruences mod primes p such that for the universal divided Bernoulli numbers . In this paper we strengthen these congruences to hold mod powers of p. 相似文献
4.
In this paper, we obtain a generalization of an identity due to Carlitz on Bernoulli polynomials. Then we use this generalized formula to derive two symmetric identities which reduce to some known identities on Bernoulli polynomials and Bernoulli numbers, including the Miki identity. 相似文献
5.
We employ the basic properties for the Hasse-Teichmüller derivatives to give simple proofs of known explicit formulae for Bernoulli numbers (of higher order) and then obtain some parallel results for their counterparts in positive characteristic. 相似文献
6.
Let q>1 and m>0 be relatively prime integers. We find an explicit period νm(q) such that for any integers n>0 and r we have
7.
The Bernoulli convolution νλ measure is shown to be absolutely continuous with L2 density for almost all , and singular if λ−1 is a Pisot number. It is an open question whether the Pisot type Bernoulli convolutions are the only singular ones. In this paper, we construct a family of non-Pisot type Bernoulli convolutions νλ such that their density functions, if they exist, are not L2. We also construct other Bernoulli convolutions whose density functions, if they exist, behave rather badly. 相似文献
9.
Kwang-Wu Chen 《Journal of Number Theory》2005,111(2):372-391
In this paper, our aim is to investigate the summation form of Bernoulli numbers Bn, such as . We derive some basic identities among them. These numbers can form a Seidel matrix. The upper diagonal elements of this Seidel matrix are called “the median Bernoulli numbers”. We determine the prime divisors of their numerators and denominators. And we characterize their ordinary generating function as the unique solution of some functional equation. At last, we also obtain the continued fraction representation of their ordinary generating function and their value of Hankel determinant. 相似文献
10.
In this paper, we define the generalized Bernoulli polynomial matrix B(α)(x) and the Bernoulli matrix B. Using some properties of Bernoulli polynomials and numbers, a product formula of B(α)(x) and the inverse of B were given. It is shown that not only B(x)=P[x]B, where P[x] is the generalized Pascal matrix, but also B(x)=FM(x)=N(x)F, where F is the Fibonacci matrix, M(x) and N(x) are the (n+1)×(n+1) lower triangular matrices whose (i,j)-entries are and , respectively. From these formulas, several interesting identities involving the Fibonacci numbers and the Bernoulli polynomials and numbers are obtained. The relationships are established about Bernoulli, Fibonacci and Vandermonde matrices. 相似文献
11.
Abdelmejid Bayad 《Journal of Number Theory》2011,131(6):1020-1036
We introduce and investigate generalized poly-Bernoulli numbers and polynomials. We state and prove several properties satisfied by these polynomials. The generalized poly-Bernoulli numbers are algebraic numbers. We introduce and study the Arakawa-Kaneko L-functions. The non-positive integer values of the complex variable s of these L-functions are expressed rationally in terms of generalized poly-Bernoulli numbers and polynomials. Furthermore, we prove difference and Raabe?s type formulae for these L-functions. 相似文献
12.
Zhi-Hong Sun 《Journal of Number Theory》2003,102(1):41-89
Let p>3 be a prime, and denote the number of solutions of the congruence . In this paper, using the third-order recurring sequences we determine the values of Np(x3+a1x2+a2x+a3) and Np(x4+ax2+bx+c), and construct the solutions of the corresponding congruences, where a1,a2,a3,a,b,c are integers. 相似文献
13.
Dongho Byeon 《Journal of Number Theory》2011,131(8):1513-1529
Let m be a positive integer and fm(x) be a polynomial of the form fm(x)=x2+x−m. We call a polynomial fm(x) a Rabinowitsch polynomial if for and consecutive integers x=x0,x0+1,…,x0+s−1, |fm(x)| is either 1 or prime. In this paper, we show that there are exactly 14 Rabinowitsch polynomials fm(x). 相似文献
14.
15.
Klaas-Tido Rühl 《Archiv der Mathematik》2008,90(3):217-222
If φ is an excellent form, then it is possible to use the dimensions of the higher complements of φ to obtain an annihilating polynomial of φ of low degree. The main result of this paper is the construction of such a polynomial with the help of methods from the theory
of generic splitting of quadratic forms.
Received: 23 April 2007 相似文献
16.
17.
In this paper we give some congruences on the r-derangement polynomials (defined below), Lah polynomials and some versions of Bell numbers and polynomials. 相似文献
18.
The difference between the 3-rank of the ideal class group
of an imaginary quadratic field
and that of the associated real quadratic field
is equal to 0 or 1. In this note, we give an infinite family of
examples in each case.Received: 9 September 2002 相似文献
19.
Research (partially) supported by Hungarian National Foundation for Scientific Research (OTKA) grant No. 273. 相似文献
20.
Let p be an odd prime and qp(a)=(ap−1−1)/p be the Fermat quotient with base a, p?a. The main purpose of this paper is to investigate the fourth power problem of qp(2) and deduce an explicit formula represented by a linear combination of Mirimanoff polynomial values. 相似文献