Related papers: A cyclic analogue of multiple zeta values

We study the algebra MD of generating function for multiple divisor sums and its connections to multiple zeta values. The generating functions for multiple divisor sums are formal power series in q with coefficients in Q arising from the…

We present several conjectures on multiple q-zeta values and on the role they play in certain problems of enumerative geometry.

We analyze certain characters of vertex algebras that can be expressed using (generalized) q-MZVs. We consider: (i) characters of vertex algebras associated to arc spaces, (ii) characters (or indices) of $\mathcal{S}$-class vertex operator…

The special values of multiple polylogarithms, which including multiple zeta values, appear some fields of mathematics and physics. Many kinds of their linear relations are investigated as well as their algebraic relations. From the…

Multiple zeta values (MZVs) are generalizations of Riemann zeta values at positive integers to multiple variable setting. These values can be further generalized to level $N$ multiple polylog values by evaluating multiple polylogs at $N$-th…

We obtain a weighted sum formula of the zeta values at even arguments, and a weighted sum formula of the multiple zeta values with even arguments and its zeta-star analogue. The weight coefficients are given by (symmetric) polynomials of…

It is shown that novel relations between multiple zeta values and single-variable multiple polylogarithms at 1/2 (delta values) can be derived by comparing two distinct, yet a priori equal, series formulae for the Drinfeld associator (from…

Ohno's relation is a well-known family of relations among multiple zeta values, which can naturally be regarded as a type of duality for a certain power series which we call an Ohno sum. In this paper, we investigate $\mathbb{Q}$-linear…

The set of multiple zeta-star values is a countable dense subset of the half line $(1,+\infty)$. In this paper, we establish some classical Diophantine type results for the set of multiple zeta-star values. Firstly, we give a criterion to…

We give an identity which is conjectured and proved by using an implementation in Multi-WZ.

We generalize Menon's identity by considering sums representing arithmetical functions of several variables. As an application, we give a formula for the number of cyclic subgroups of the direct product of several cyclic groups of arbitrary…

Through the application of an evaluation technique based on cyclotomic multiple zeta values recently due to Au, we solve open problems on inverse binomial series that were included in a 2010 analysis textbook by Chen.

We define the interpolated polynomial multiple zeta values as a generalization of all of multiple zeta values, multiple zeta-star values, interpolated multiple zeta values, symmetric multiple zeta values, and polynomial multiple zeta…

In a recent paper, A. Libgober showed that the multiplicative sequence {Q_i(c_1,...,c_i)} of Chern classes corresponding to the power series Q(z)=1/Gamma(1+z) appears in a relation between the Chern classes of certain Calabi-Yau manifolds…

The multiple zeta values (MZVs) possess a rich algebraic structure of algebraic relations, which is conjecturally determined by two different (shuffle and stuffle) products of a certain algebra of noncommutative words. In a recent work,…

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…

In this paper we use the generating functions and the double shuffle relations satisfied the multiple zeta values to derive some new families of identities.

We establish an identity amongst certain differential operators applied to a formal power-series. As a corollary we obtain an explicit depth reduction result for alternating MZV's of the form $\zeta(1,\ldots,1,\overline{2m})$, which…

We propose a relation between values of the Riemann zeta function $\zeta$ and a family of integrals. This results in an integral representation for $\zeta(2p)$, where $p$ is a positive integer, and an expression of $\zeta(2p+1)$ involving…

Ohno's relation is a well-known relation among multiple zeta values.In this paper, we prove Ohno-type relation for finite multiple zeta values, which is conjectured by Kaneko.As a corollary, we give an alternative proof of the sum formula…