Related papers: On generalizations of the sum formula for multiple…
Interpolated multiple $q$-zeta values are deformation of multiple $q$-zeta values with one parameter, $t$, and restore classical multiple zeta values as $t = 0$ and $q \to 1$. In this paper, we discuss generating functions for sum of…
We consider a cyclic analogue of multiple zeta values (CMZVs), which has two kinds of expressions; series and integral expression. We prove an `integral$=$series' type identity for CMZVs. By using this identity, we construct two classes of…
In [Ok] Okounkov studies a specific $q$-analogue of multiple zeta values and makes some conjectures on their algebraic structure. In this note we compare Okounkovs $q$-analogues to the generating function for multiple divisor sums defined…
We investigate an arithmetic function representing a generalization of the gcd-sum function, considered by Kurokawa and Ochiai in 2009 in connection with the multivariable global Igusa zeta function for a finite cyclic group. We show that…
In this paper we present many new families of identities for multiple harmonic sums using binomial coefficients. Some of these generalize a few recent results of Hessami Pilehrood et al. As applications we prove several conjectures…
We define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In particular, we establish several explicit formulas of (Hurwitz) zeta functions,…
The Ohno relation is a well known relation in the theory of multiple zeta values. Recently, Seki and Yamamoto introduced a connector method and gave its succinct proof. On the other hand, Igarashi obtained the generalization of the Ohno…
We prove that any Mordell-Tornheim sum with positive integer arguments can be expressed as a rational linear combination of multiple zeta values of the same weight and depth. By a result of Tsumura, it follows that any Mordell-Tornheim sum…
In this paper, we establish some reciprocity formulas for certain generalized Hardy-Berndt sums by using the Fourier series technique and some properties of the periodic zeta function and the Lerch zeta function. It turns out that one of…
We show that any convergent (shuffle) arborified zeta value admits a series representation. This justifies the introduction of a new generalisation to rooted forests of multiple zeta values, and we study its algebraic properties. As a…
Inspired by the theory of Hodge correlators due to Goncharov and by the plectic principle of Nekov\'a\v{r} and Scholl, we construct higher plectic Green functions and give a higher order generalization of Hecke's formula for abelian…
Kawashima's relation is conjecturally one of the largest classes of relations among multiple zeta values. Gaku Kawashima introduced and studied a certain Newton series, which we call the Kawashima function, and deduced his relation by…
We exploit transformations relating generalized $q$-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such as $\pi$, and to connect sums…
Multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types are known as generalizations of the Riemann zeta function. In 2018, Kaneko and Tsumura proved that the multiple zeta functions of Arakawa-Kaneko type can be expressed as a…
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}…
Recently, Bradley studied partial sums of multiple q-zeta values and proved a duality result. In this paper, we present a generalization of his result.
This paper presents the evaluation of the Euler sums of generalized hyperharmonic numbers $H_{n}^{\left( p,q\right) }$ \[ \zeta_{H^{\left( p,q\right) }}\left( r\right) =\sum\limits_{n=1}^{\infty }\dfrac{H_{n}^{\left( p,q\right) }}{n^{r}}%…
Interpolated multiple zeta values can be regarded as interpolation polynomials of multiple zeta values and multiple zeta-star values. In this paper, we give some algebraic relations of interpolated multiple zeta values, such as the…
Ramanujan sums have been studied and generalized by several authors. For example, Nowak studied these sums over quadratic number fields, and Grytczuk defined that on semigroups. In this note, we deduce some properties on sums of generalized…
Relying on the Hurwitz formula, we find sums of the series over sine and cosine functions through the Hurwitz zeta function. Using another summation formula for these trigonometric series, we find finite sums of some series over the Riemann…