Related papers: Iterated integrals and relations of multiple polyl…
The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable Quantum Field Theories requires extensions of multiply nested harmonic sums, which can be generated as real representations by Mellin…
It was shown in that harmonic numbers satisfy certain reciprocity relations, which are in particular useful for the analysis of the quickselect algorithm. The aim of this work is to show that a reciprocity relation from…
In this review article, we report on some recent advances on the computational aspects of cohomology intersection numbers of GKZ systems developed in \cite{GM}, \cite{MH}, \cite{MT} and \cite{MT2}. We also discuss the relation between…
In this paper we give two idelic representations of the multiple zeta values - one using iterated integrals over the finite ideles and the other using iterated integrals over the idele class group. Each of the representations leads to a…
We generalize the well-known parity theorem for multiple zeta values (MZV) to functional equations of multiple polylogarithms (MPL). This reproves the parity theorem for MZV with an additional integrality statement, and also provides parity…
It is known that solutions of the KZ equations can be written in the form of multidimensional hypergeometric integrals. In 2017 in a joint paper of the author with V. Schechtman the construction of hypergeometric solutions was modified, and…
In this article, we set up a method of reconstructing to polylogarithms $\mathrm{Li}_k(z)$ from zeta values $\zeta(k)$ via the Riemann-Hilbert problem. This is referred to as "a recursive Riemann-Hilbert problem of additive type." Moreover,…
In this paper, we define finite Carlitz multiple polylogarithms and show that every finite multiple zeta value over the rational function field $\mathbb{F}_{q}(\theta)$ is an $\mathbb{F}_{q}(\theta)$-linear combination of finite Carlitz…
We introduce a $q$-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple $q$-zeta values satisfy a $q$-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the…
Multiple $T$-values, a variant of multiple zeta values of level two, were introduced and studied by Kaneko and Tsumura. This paper will introduce iterated log-tangent integrals and discuss their relations with multiple $T$-values. We will…
The main goal of this paper is to study properties of the iterated integrals of modular forms in the upper halfplane, eventually multiplied by $z^{s-1}$, along geodesics connecting two cusps. This setting generalizes simultaneously the…
In this paper, the extended double shuffle relations for interpolated multiple zeta values are established. As an application, Hoffman's relations for interpolated multiple zeta values are proved. Furthermore, a generating function for sums…
We have gone back to old methods found in the historical part of Hardy's Divergent Series well before the invention of the modern analytic continuation to use formal manipulation of harmonic sums which produce some interesting formulae.…
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…
In this note we introduce multi-interpolated multiple zeta values. We provide a basic decomposition of these objects involving ordered partitions. We also obtain identities for special instances of multi-interpolated multiple zeta values…
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…
The purpose of this paper is two-fold. First, we consider the classical Mordell--Tornheim zeta values and their alternating version. It is well-known that these values can be expressed as rational linear combinations of multiple zeta values…
In this paper, we give a natural construction of mixed Tate motives whose periods are a class of iterated integrals which include the multiple polylogarithm functions. Given such an iterated integral, we construct two divisors $A$ and $B$…
We give a representation of the classical Riemann $\zeta$-function in the half plane $\Re s>0$ in terms of a Mellin transform involving the real part of the dilogarithm function with an argument on the unit circle (associated Clausen…
The cyclic relation obtained in a study by Hirose, Murakami, and the first-named author, is a wide class of relations, which includes the well-known cyclic sum formula for multiple zeta and zeta-star values, and the derivation relation for…