Related papers: Relationship between renormalized values of shuffl…

In this paper we consider iterated integrals on $\mathbb{P}^{1}\setminus\{0,1,\infty,z\}$ and define a class of $\mathbb{Q}$-linear relations among them, which arises from the differential structure of the iterated integrals with respect to…

We consider multi-polylogarithm functions which are slightly different from the ordinary ones. These functions have two integral representations and an order structure similar to those of multiple zeta star values. We also give a necessary…

We consider a generalization of elliptic multiple zeta values, which we call twisted elliptic multiple zeta values. These arise as iterated integrals on an elliptic curve from which a rational lattice has been removed. At the cusp, twisted…

In this work, it is introduced a new function based on the non-trivial zeros of the Riemann-zeta function. Such function shows an interesting behavior: when the argument of the function grows, it changes from a pseudo-random behavior to a…

This paper develops an approach to the evaluation of quadratic Euler sums that involve harmonic numbers. The approach is based on simple integral computations of polyloga- rithms. By using the approach, we establish some relations between…

We provide a framework for relating certain q-series defined by sums over partitions to multiple zeta values. In particular, we introduce a space of polynomial functions on partitions for which the associated q-series are q-analogues of…

It is known that multiple zeta values can be written in terms of certain iterated log-sine integrals. Conversely, we evaluate iterated log-sine integrals in terms of multiple polylogarithms and multiple zeta values in this paper. We also…

The hyperharmonic numbers h_{n}^{(r)} are defined by means of the classical harmonic numbers. We show that the Euler-type sums with hyperharmonic numbers: {\sigma}(r,m)=\sum_{n=1}^{\infty}((h_{n}^{(r)})/(n^{m})) can be expressed in terms of…

In this paper we shall develop a theory of (extended) double shuffle relations of Euler sums which generalizes that of multiple zeta values (see Ihara, Kaneko and Zagier, \emph{Derivation and double shuffle relations for multiple zeta…

The main object of this paper is to obtain several symmetric properties of the q-Zeta type functions. As applications of these properties, we give some new interesting identities for the modified q-Genocchi polynomials. Finally, our…

A large family of relations among multiple zeta values may be described using the combinatorics of shuffle and quasi-shuffle algebras. While the structure of shuffle algebras have been well understood for some time now, quasi-shuffle…

We introduce a new generalization of Stirling numbers of the second kind and analyze their properties, including generating functions, integral representations, and recurrence relations. These numbers are used to approximate Riemann zeta…

A brief survey of the zeta function regularization and multiplicative anomaly issues when the associated zeta function of fluctuation operator is the regular at the origin (regular case) as well as when it is singular at the origin…

In this article, we will prove the Giambelli formula for Schur multiple zeta-functions of extended shape which we call laced type, using the combinatorial method of proving the Giambelli formula for Schur function by Egecioglu and Remmel.…

We will introduce a regularization for $p$-adic multiple zeta values and show that the generalized double shuffle relations hold. This settles a question raised by Deligne, given as a project in Arizona winter school 2002. Our approach is…

A scaling and renormalization approach to the Riemann zeta function, $\zeta$, evaluated at $-1$ is presented in two ways. In the first, one takes the difference between $U_{n}:=\sum_{q=1}^{n}q$ and $4U_{\left\lfloor \frac{n}{2}\right\rfloor…

In this paper we study multiple Dedekind symbols and the associated multiple reciprocity functions. There is a bijection between the two sets of them after a normalization. By this bijection we define products of multiple reciprocity…

We introduce a theory of probabilistic renormalization for series, the renormalized values being encoded in the expectation of a certain random variable on the set of natural numbers. We identify a large class of weakly renormalizable…

We obtain a class of quadratic relations for a q-analogue of multiple zeta values (qMZV's). In the limit q->1, it turns into Kawashima's relation for multiple zeta values. As a corollary we find that qMZV's satisfy the linear relation…

The $t$-adic symmetric multiple zeta values were defined Jarossay, which have been studied as a real analogue of $\boldsymbol{p}$-adic finite multiple zeta values. In this paper, we consider the star analogues based on several…