Related papers: Derivation relation for finite multiple zeta value…
We establish a generalized Ihara zeta function formula for simple graphs with bounded degree. This is a generalization of the formula obtained by G. Chinta, J. Jorgenson and A. Karlsson from a vertex-transitive graph.
In this paper we prove some new identities for multiple zeta values and multiple zeta star values of arbitrary depth by using the methods of integral computations of logarithm function and iterated integral representations of series. By…
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…
The even weight period polynomial relations in the double shuffle Lie algebra $\mathfrak{ds}$ were discovered by Ihara, and completely classified by the second author by relating them to restricted even period polynomials associated to cusp…
The multiple zeta values (MZV) are a set of real numbers with a beautiful structure as an algebra over the rational numbers. They are related to maybe the most important conjecture on mathematics today, the Riemann hypothesis. In this paper…
Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then,…
The relationship between the Ohno relation and multiple polylogarithms are discussed. Using this relationship, the algebraic reduction of the Ohno relation is given.
The aim of this work is an analytic investigation of differential equations producing mirror maps as well as giving new examples of mirror maps; one of these examples is related to (rational approximations to) $\zeta(4)$. We also indicate…
The conical zeta values are a generalization of the multiple zeta values which are defined by certain multiple sums over convex cones. In this paper, we present a relation between the values of the Dedekind zeta functions for totally real…
Gangl, Kaneko, and Zagier gave explicit linear relations among double zeta values of odd indices coming from the period polynomials of modular forms for ${\rm SL}(2,\mathbb{Z})$. In this paper, we generalize their result to the linear…
We present several formulas for some specific multiple $L$-values of conductor four. This grew out from the study of zeta functions of level four of Arakawa-Kaneko type. Closely related is a new version of multiple poly-Euler numbers and we…
In this paper, we discuss the parity result for multiple Dirichlet series which contains some special values of multiple zeta functions as special cases, Mordell--Tornheim type of multiple zeta values, zeta values of the root systems and so…
We consider fuzzy valued functions from two parametric representations of $\alpha$-level sets. New concepts are introduced and compared with available notions. Following the two proposed approaches, we study fuzzy differential equations.…
We study a class of q-analogues of multiple zeta values given by certain formal q-series with rational coefficients. After introducing a notion of weight and depth for these q-analogues of multiple zeta values we present dimension…
We study a certain class of q-analogues of multiple zeta values, which appear in the Fourier expansion of multiple Eisenstein series. Studying their algebraic structure and their derivatives we propose conjectured explicit formulas for the…
In this note, we prove the existence of infinitely many zeros of certain generalized Hurwitz zeta functions in the domain of absolute convergence. This is a generalization of a classical problem of Davenport, Heilbronn and Cassels about the…
Ohno's relation is a well known formula among multiple zeta values. In this paper, we present its interpolation to complex functions.
Following Bachmann's recent work on bi-brackets and multiple Eisenstein series, Zudilin introduced the notion of multiple q-zeta brackets, which provides a q-analog of multiple zeta values possessing both shuffle as well as quasi-shuffle…
In this paper we study the derived sets for the rational deformations of multiple zeta-star values. By using the theory of bounded variation functions, we will give function decompositions which describe the metric structure of the derived…
Hirose, Murahara, and Saito proved that some $t$-adic symmetric multiple zeta values, for indices in which $1$ and $3$ appear alternately in succession, can be expressed as polynomials in Riemann zeta values, and conjectured similar…