In this paper we present some new binomial identities for multiple harmonic sums whose
indices are the sequences $(\{1\}^ a, c,\{1\}^ b), $$(\{2\}^ a, c,\{2\}^ b) $ and prove a number …

On some congruences involving Domb numbers and harmonic numbers 1. Introduction Recall
that the Bernoulli numbers {Bn}n≥0 and Page 1 International Journal of Number Theory Vol …

We collect here 100 open conjectures on congruences made by the author, some of which
have never been published. This is a new edition of the author's preprint arXiv: 0911.5665 …

Dirichlet's $ L $-functions are natural extensions of the Riemann zeta function. In this paper
we first give a brief survey of Ap\'ery-like series for some special values of the zeta function …

We introduce and study a``level two''analogue of finite multiple zeta values. We give
conjectural bases of the space of finite Euler sums as well as that of usual finite multiple zeta …

In this paper, we mainly prove the following conjectures of Sun ZH (New congruences
involving Apéry-like numbers. Preprint at arXiv: 2004.07172 v2): Let p> 3 be a prime. Then A …

In 2010, Kh. Hessami Pilehrood and T. Hessami Pilehrood introduced generating function
identities used to obtain series accelerations for values of Dirichlet's β function, via the …

1. Introduction Page 1 Congruences involving Franel numbers and Apéry-like numbers Guo-Shuai
Mao Department of Mathematics, Nanjing University of Information Science and Technology …

In this paper, we study congruences on sums of products of binomial coefficients that can be
proved by using properties of the Jacobi polynomials. We give special attention to …

The quadrinomial coefficient is defined as the coefficient of x< sup> k in the polynomial
expansion of 1+ x+ x²+ x³)< sup> n, where n and k are nonnegative integers. In the present …