Related papers: Ohno relation for regularized refined symmetric mu…

We consider iterated integrals of $\log\zeta(s)$ on certain vertical and horizontal lines. Here, the function $\zeta(s)$ is the Riemann zeta-function. It is a well known open problem whether or not the values of the Riemann zeta-function on…

We construct an analytic approach to evaluate odd Euler sums, multiple zeta value $\zeta(3,2,\ldots,2)$ and multiple $t$-value $t\left(3,2,\ldots,2\right)$. Moreover, we also conjecture a closed expression for multiple $t$-value…

We prove a sum formula with 4 parameters among finite alternating multiple zeta values which can be regarded as an alternating version of the result of Kamano on finite multiple zeta values.

We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some…

The $t$-adic symmetric multiple zeta value is a generalization of the symmetric multiple zeta value from the perspective of the Kaneko-Zagier conjecture. In this paper, we introduce a further generalization with a new parameter $s$, which…

Ihara, Kaneko, and Zagier proved the derivation relation for multiple zeta values. The first named author obtained its counterpart for finite multiple zeta values in $\mathcal{A}$. In this paper, we present its generalization in…

It is pointed out that the generalized Lambert series $\displaystyle\sum_{n=1}^{\infty}\frac{n^{N-2h}}{e^{n^{N}x}-1}$ studied by Kanemitsu, Tanigawa and Yoshimoto can be found on page $332$ of Ramanujan's Lost Notebook in a slightly more…

By introducing a generalized notion of multiple zeta values associated with an arbitrary finite subset $S\subset \mathbb{P}^1(\mathbb{C})$ and studying their transformation properties under rational functions, we show that multiple…

We establish a new class of relations among the multiple zeta values \zeta(k_1,k_2,...,k_n), which we call the cyclic sum identities. These identities have an elementary proof, and imply the "sum theorem" for multiple zeta values. They also…

It is conjectured that the regularized double shuffle relations give all algebraic relations among the multiple zeta values, and hence all other algebraic relations should be deduced from the regularized double shuffle relations. In this…

The renormalization of MZV was until now carried out by algebraic means. We show that renormalization in general, of the multiple zeta functions in particular, is more than mere convention. We show that simple calculus methods allow us to…

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…

We introduce the multivariable connected sum which is a generalization of Seki-Yamamoto's connected sum and prove the fundamental identity for these sums by series manipulation. This identity yields explicit procedures for evaluating…

The values of the Riemann zeta function at odd positive integers, $\zeta(2n+1)$, are shown to admit a representation proportional to the finite-part of the divergent integral $\int_0^{\infty} t^{-2n-1} \operatorname{csch}t\,\mathrm{d}t$.…

The derivation relations for multiple zeta values is proved by Ihara, Kaneko and Zagier. We prove its counterpart for finite multiple zeta values.

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…

There are many results for explicit expressions about $q$-multiple zeta values or $q$-harmonic sums on $A-\cdots-A$ indices, that is, the indices are the same. Though the way to treat $q$-multiple zeta values unless the indices are the…

We study multiple zeta values and their generalizations from the point of view of Rota--Baxter algebras. We obtain a general framework for this purpose and derive relations on multiple zeta values from relations in Rota--Baxter algebras.

In this work we discuss a parameter $\sigma$ on weighted $k$-element multisets of $[n]= \{1,\dots ,n\}$. The sums of weighted $k$-multisets are related to $k$-subsets, $k$-multisets, as well as special instances of truncated interpolated…

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…