Related papers: The Multiple Zeta Value Data Mine

In this article, we introduce an algebraic setup of non-strict multiple zeta values (NMZVs, for short) and prove some relations of NMZVs, which are analogous to Hoffman's relations of multiple zeta values, by using this algebraic setup of…

In this paper we consider iterated integrals of multiple polylogarithm functions and prove some explicit relations of multiple polylogarithm functions. Then we apply the relations obtained to find numerous formulas of alternating multiple…

This paper offers a Hopf algebraic interpretation of a functional equation of multiple zeta functions, motivated by the classical symmetry of the Riemann zeta function. Starting from the extended shuffle algebra that encodes multiple zeta…

We introduce "puzzles of quasi-finite type" which are the counterparts of our subshifts of quasi-finite type (Invent. Math. 159 (2005)) in the setting of combinatorial puzzles as defined in complex dynamics. We are able to analyze these…

We investigate relations between elliptic multiple zeta values and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based on representing elliptic multiple zeta values as iterated…

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…

Multizeta values are numbers appearing in many different contexts. Unfortunately, their arithmetics remains mostly out of reach. In this article, we define a functional analogue of the algebra of multizetas values, namely the algebra of…

In this paper we introduce confluence relations for motivic Euler sums (also called alternating multiple zeta values) and show that all linear relations among motivic Euler sums are exhausted by the confluence relations. This determines all…

In the study of order estimation of the Riemann zeta-function $ \zeta(s) = \sum_{n=1}^\infty n^{-s} $, solving Lindel\"{o}f hypothesis is an important theme. As one of the relationships, asymptotic behavior of mean values has been studied.…

The multiple zeta values are multivariate generalizations of the values of the Riemann zeta function at positive integers. The Bowman-Bradley theorem asserts that the multiple zeta values at the sequences obtained by inserting a fixed…

Weighted twin support vector machines (WLTSVM) mines as much potential similarity information in samples as possible to improve the common short-coming of non-parallel plane classifiers. Compared with twin support vector machines (TWSVM),…

I define multiple Watson values (MWVs) as iterated integrals, on the interval $x\in[0,1]$, of the 6 differential forms $A=d\log(x)$, $B=-d\log(1-x)$, $T=-d\log(1-z_1x)$, $U=-d\log(1-z_2x)$, $V=-d\log(1-z_3x)$ and $W=-d\log(1-z_4x)$, where…

In this paper, we give an elementary account into Zagier's formula for multiple zeta values involving Hoffman elements. Our approach allows us to obtain direct proof in a special case via rational zeta series involving the coefficient…

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…

Multiple zeta values arise as special values of polylogarithms defined on Riemann surfaces of various genera. Building on the vast knowledge for classical and elliptic multiple zeta values, we explore a canonical extension of the formalism…

Formal multiple zeta values allow to study multiple zeta values by algebraic methods in a way that the open question about their transcendence is circumvented. In this note we show that Hoffman's basis conjecture for formal multiple zeta…

Multiples zeta values and alternating multiple zeta values in positive characteristic were introduced by Thakur and Harada as analogues of classical multiple zeta values of Euler and Euler sums. In this paper we determine all linear…

In this paper, we generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give…

Multiple zeta values have been studied by a wide variety of methods. In this article we summarize some of the results about them that can be obtained by an algebraic approach. This involves "coding" the multiple zeta values by monomials in…

We show the recurrence relations of the Euler-Zagier multiple zeta-function which describes the $r$-fold function with one variable specialized to a non-positive integer as a rational linear combination of $(r-1)$-fold functions, which…