Related papers: Stern's type congruences for L(-k,\chi)

We give two congruence properties of Hermitian modular forms of degree 2 over $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-3})$. The one is a congruence criterion for Hermitian modular forms which is generalization of Sturm's theorem.…

Stanley, building on work of Stern, defined an array of numbers by the recurrence $s(n, 2k) = s(n-1, k)$, $s(n, 2k+1) = s(n-1, k) + s(n-1, k+1)$. Stanley showed that, for each positive integer $r$, the sequence $s_n^r:= \sum_k s(n,k)^r$…

We give a determination of the equivalence group of Euler-Bernoulli equation and of one of its generalizations, and thus derive some symmetry properties of this equation.

We prove Jacobi-Trudi-type determinantal formulas for skew dual Grothendieck polynomials which are $K$-theoretic deformations of Schur polynomials. We also prove a bialternant-type formula analogous to the classical definition of Schur…

We study matrices which transform the sequence of Fibonacci or Lucas polynomials with even index to those with odd index and vice versa. They turn out to be intimately related to generalized Stirling numbers and to Bernoulli, Genocchi and…

The relations between the Bernoulli and Eulerian polynomials of higher order and the complete Bell polynomials are found that lead to new identities for the Bernoulli and Eulerian polynomials and numbers of higher order. General form of…

Let $B_{n}$ denote the Bernoulli numbers, and $S(n,k)$ denote the Stirling numbers of the second kind. We prove the following identity $$ B_{m+n}=\sum_{\substack{0\leq k \leq n \\ 0\leq l \leq m}}\frac{(-1)^{k+l}\,k!\, l!\,…

In this paper, we give some interesting and new identities of q-Bernoulli numbers which are derived from convolutions on the ring of p-adic integers.

Sequences of Genocchi numbers of the first and second kind are considered. For these numbers, an approach based on their representation using sequences of polynomials is developed. Based on this approach, for these numbers some identities…

In this paper, we present a sufficient condition on a pair of nonnegative weights $v$ and $w$ such that we have a general weighted $L^{p}$-Hardy type identity. The result, for a certain choice of weights, gives weighted $L^{p}$-Hardy type…

In this paper, we consstruct a new extended q-Bernoulli numbers and poly nomials. From these numbers, we derive the multiple zeta functions and give some relations between multiple Bernoulli numbers and multiple zeta functions.

We prove a duality formula for certain sums of values of poly-Bernoulli polynomials which generalizes dualities for poly-Bernoulli numbers. We first compute two types of generating functions for these sums, from which the duality formula is…

We give an elementary and self-contained proof of the equivalence of a collection of Wolstenholme-type congruences due to Helou and Terjanian.

We extend some results known for the K\"ahler-Ricci flow to the Chern-Ricci flow regarding the independence of singularity types for long-time solutions. Specifically, we show that if a solution to the Chern-Ricci flow exists with uniformly…

Osburn, Sahu and Straub introduced the numbers: \begin{align*} A_n^{(r,s,t)}=\sum_{k=0}^n{n\choose k}^r{n+k\choose k}^s{2k\choose n}^t, \end{align*} for non-negative integers $n,r,s,t$ with $r\ge 2$, which includes two kinds of Ap\'ery…

We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.

Using general identities for difference operators, as well as a technique of symbolic computation and tools from probability theory, we derive very general kth order (k \ge 2) convolution identities for Bernoulli and Euler polynomials. This…

An occurrence of a classical pattern p in a permutation \pi is a subsequence of \pi whose letters are in the same relative order (of size) as those in p. In an occurrence of a generalized pattern, some letters of that subsequence may be…

We introduce poly-Bernoulli polynomials in two variables by using a generalization of Stirling numbers of the second kind that we studied in a previous work. We prove the bi-variate poly-Bernoulli polynomial version of some known results on…

In this paper, we present k sequences of Generalized Van der Laan Polynomials and Generalized Perrin Polynomials using Genaralized Fibonacci and Lucas Polynomials. We give some properties of these polynomials. We also obtain generalized…