Related papers: Stern's type congruences for L(-k,\chi)
Recently, the two variable $q$-$L$-functions which interpolate the generalized $q$-Bernoulli polynomials associated with $\chi$ are introduced and studied, cf. [2]. In this paper, we construct multiple Dirichlet's $q$-$L$-function which…
In this work, we determined the general terms of all almost balancing numbers of first and second type in terms of balancing numbers and conversely we determined the general terms of all balancing numbers in terms of all almost balancing…
Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in…
In this paper, we give the determinant expressions of the hypergeometric Bernoulli numbers, and some relations between the hypergeometric and the classical Bernoulli numbers which include Kummer's congruences. By applying Trudi's formula,…
Let $NT(m, k, n)$ denote the total number of parts in the partitions of n with rank congruent to m modulo k. Andrews proved Beck's conjecture on congruences for $NT(m, k, n)$ modulo 5 and 7. Generalizing Andrews'results, Chern obtain…
In this article, we achieve some general statistical approximation results for $ \lambda $-Bernstein operators in addition to some other approximation properties. We prove a statistical Voronovskaja-type approximation theorem. We also…
We give an improvement of a result of J. Martinet on Stickelberger's congruences for the absolute norms of relative discriminants of number fields, by using classical arguments of class field theory.
Using techniques due to Coster, we prove a supercongruence for a generalization of the Domb numbers. This extends a recent result of Chan, Cooper and Sica and confirms a conjectural supercongruence for numbers which are coefficients in one…
Hurwitz numbers are the Laurent coefficients of an elliptic function $\wp(u)$ of cyclotomic type, and they are natural generalization of the Bernoulli numbers. This paper gives new generalization of Bernoulli and Hurwitz numbers for higher…
We give a new proof of Chen-Lin result with Li-Zhang method.
In this paper, we generalise a congruence which proved by V. J.-W. Guo and J. Zeng \cite{gz-jnt-2012} involving Ap\'{e}ry numbers, and we obtain a congruence involving Franel numbers which confirms a congruence conjecture of Z.-W. Sun…
We mainly show a supercongruence for a truncated series with cubes of Catalan numbers which extends a result by Zhi-Wei Sun.
Based on a $q$-congruence of the author and Petrov, we set up a $q$-analogue of Sun--Tauraso's congruence for sums of Catalan numbers, which extends a $q$-congruence due to Tauraso.
By considering Eulerian numbers and ordered Stirling numbers of the second and third kinds over a multiset, we generalize identities of Eulerian numbers and Stirling numbers of the second and third kinds and provide $q$-analogs of these…
We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…
In this paper some Tur\'an type inequalities for classical and generalized Mittag-Leffler functions are considered. The method is based on proving monotonicity for special ratio of sections for series of Mittag-Leffler functions. Some…
In the paper, the authors establish an explicit formula for computing Bernoulli polynomials at non-negative integer points in terms of $r$-Stirling numbers of the second kind.
In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…
In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. We give also some identities linked the…
In this paper we generalize the approximation theorem for L^2-Betti numbers to an approximation theorem for center-valued Betti-numbers.