Related papers: $p$-adic multiple zeta values and binomial multipl…

Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…

The purpose of this paper is to give the explicit formulae of p-adic l-functions and sums of powers which are related to Euler numbers.

The p-adic valuation of a polynomial can be given by its valuation tree. This work describes the 2-adic valuation tree of the general degree 2 polynomial in 2 variables.

During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured $p$-adic analogues to such formulae. Using a combination…

We derive various weighted summation identities, including binomial and double binomial identities, for Tribonacci numbers. Our results contain some previously known results as special cases.

In this paper we establish several recurrence relations about Euler-Ap\'ery type multiple zeta star values and a parametric variant of it by using the method of iterated integrals. Then using the formulas obtained, we find the explicit…

We obtain recursive formulas for the stuffle product of multiple zeta values and of multiple zeta-star values. Then we apply the formulas to prove several stuffle product formulas with one or two strings of $z_p$'s. We also describe how to…

We introduce a symbolic representation of $r$-fold harmonic sums at negative indices. This representation allows us to recover and extend some recent results by Duchamp et al., such as recurrence relations and generating functions for these…

We study two families of zeta-like multiple series -- the multiple $\rho$-values and the multiple $\eta$-values -- defined by nested sums with shifted denominators. An explicit factorial formula for $\rho$ reveals its intrinsic…

We present several sequences involving harmonic numbers and the central binomial coefficients. The calculational technique is consists of a special summation method that allows, based on proper two-valued integer functions, to calculate…

Taking inspiration from the work of Lanphier \cite{LANPHIER2022125716}, a generalized multivariable polynomial formulation for sums of alternating powers is given, as well as analogous sums. Furthermore, an analog of the Euler-Maclaurin…

The definition for the $p$-adic Hurwitz-type Euler zeta functions has been given by using the fermionic $p$-adic integral on $\mathbb Z_p$. By computing the values of this kind of $p$-adic zeta function at negative integers, we show that it…

For $k\leq n$, let $E(mn,k)$ be the sum of all multiple zeta values of depth $k$ and weight $mn$ with arguments are multiples of $m\geq 2$. More precisely, $E(mn,k)=\sum_{|\boldsymbol{\alpha}|=n}\zeta(m\alpha_1,m\alpha_2,\ldots,…

\medskip\noindent\textbf{R\'esum\'e.} Soit $l$ un entier et $\ors=(s_1, \dots, s_l)$ une s\'equence d'entiers positifs. Dans ce document, nous \'etudierons les propri\'et\'es arithm\'etique de sommes harmoniques multiples $H(\ors; n)$, qui…

We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…

The Newton series which interpolate finite multiple harmonic sums are useful in the study of multiple zeta values (MZV's). In this paper, we prove that these Newton series can be written as multiple series. As an application, we give a…

In this paper, we introduce zeta values of rational convex cones, which is a generalization of cyclotomic multiple zeta values. These zeta values have integral expressions. The main theorem asserts that zeta values of cones can be expressed…

Let Q(4n,d) be the sum of all multiple zeta values of depth d and weight 4n whose arguments are all multiples of 4. In this paper we derive a formula of Q(4n,d) for all d>2 as a finite sum involving binomial coefficients, Bernoulli numbers…

In this paper, we obtain a restricted decomposition formula for interpolated multiple zeta values using t-stuffle product. We then derive a recursive formula of t-stuffle product, which also provides a route to the same formula. In both…

For a pair of positive integers $n,k$ with $n\geq 2$, in this paper we prove that $$ \sum_{r=1}^k\sum_{|\bf\alpha|=k}{k\choose\bf\alpha} \zeta(n\bf\alpha)=\zeta(n)^k =\sum^k_{r=1}\sum_{|\bf\alpha|=k}…