Related papers: Stern's type congruences for L(-k,\chi)
The main object of this paper is to investigate a new class of the generalized Hurwitz type poly-Bernoulli numbers and polynomials from which we derive some algorithms for evaluating the Hurwitz type poly-Bernoulli numbers and polynomials.…
A recent result of G. Cz\'edli relates the ordered set of principal congruences of a bounded lattice $L$ with the ordered set of principal congruences of a~bounded sublattice $K$ of $L$. In this note, I sketch a new proof.
This note presents criteria in terms of Bernoulli numbers for a number to be simultaneously a Wilson prime and a Lerch prime.
A treatment of (generalized) Clemens-Schmid exact sequences from the perspective of weights.
This paper is devoted to establishing several new formulas relating Bernoulli and Stirling numbers of both kinds.
We prove the equivalence between the several notions of generalized Ricci curvature found in the literature. As an application, we characterize when the total generalized Ricci tensor is symmetric.
In this paper, we define k-generalized order-k numbers and we obtain a relation between i-th sequences and k-th sequences of k-generalized order-k numbers. We give some determinantal and permanental representations of k-generalized order-k…
In this brief note, we give two explicit formulas for the Bernoulli Numbers in terms of the Stirling numbers of the second kind, and the Eulerian Numbers. To the best of our knowledge, these formulas are new. We also derive two more…
In the paper, the authors find two closed forms involving the Stirling numbers of the second kind and in terms of a determinant of combinatorial numbers for the Bernoulli polynomials and numbers.
We summarize results concerning the Bernstein property of differential equations.
The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.
We investigate Eisenstein congruences between the so-called Euler systems of Garrett--Rankin--Selberg type. This includes the cohomology classes of Beilinson--Kato, Beilinson--Flach and diagonal cycles. The proofs crucially rely on…
In a recent preprint on ArXiv, Bacher introduced a twisted version of the Stern sequence. His paper contains in particular three conjectures relating the generating series for the Stern sequence and for the twisted Stern sequence. Soon…
The recent interest in $q$-Stirling numbers of the second kind in type B prompted us to give a type B analogue of a classical identity connecting the $q$-Stirling numbers of the second kind and Carlitz's major $q$-Eulerian numbers, which…
First, we shall formulate and prove Theorem of Lie-Kolchin type for a cone and derive some algebro-geometric consequences. Next, inspired by a recent result of Dinh and Sibony we pose a conjecture of Tits type for a group of automorphisms…
In this paper we attack the Erdos-Straus conjecture by means of the structure of its solutions, extending and improving the results of a previous paper. Using previous results and supported by the works of Elsholtz and Tao and Monks and…
In this paper, we use our previous study of the higher order Bernoulli numbers $B_n^{(l)}$ to investigate the $p$-adic properties of the Stirling numbers of the second kind $S(n,k)$. For example, we give a new, greatly simplified proof of…
We investigate some interesting properties of Bernstein polynomials associated with boson p-adic integrals on Zp.
Recently, Kim-Jang-Yi have introduced q-Bernstein polynomials. From these q-Berstein polynomials, we investigte some properties related to q-Stirling numbes and q-Bernoulli numbes.
Let B_n denote the nth Bell number. We use well-known recursive expressions for B_n to give a generalizing recursion that can be used to prove Touchard's congruence.