Related papers: On generalized stuffle relations between cell-zeta…
In this paper, we study some Euler-Ap\'ery-type series which involve central binomial coefficients and (generalized) harmonic numbers. In particular, we establish elegant explicit formulas of some series by iterated integrals and…
The purpose this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials and we construct multiple q-zeta function which interpolates multiple q-Euler numbers at negative integers.
In recent years, a variety of variants of multiple zeta values (MZVs) have been defined and studied. One way to produce these variants is to restrict the indices in the definition of MZVs to some fixed parity pattern, which include…
Multiple zeta values (MZVs) in the usual sense are the special values of multiple variable zeta functions at positive integers. Their extensive studies are important in both mathematics and physics with broad connections and applications.…
Using the Semple bundle construction, we derive an intersection-theoretic formula for the number of simultaneous contacts of specified orders between members of a generic family of degree $d$ plane curves and finitely many fixed curves. The…
It is widely accepted nowadays that polyzetas are connected by polynomial relations. One way to obtain relations among polyzetas is to consider their generating series and the relations among these generating series. This leads to the…
We give a simple generalisation of a theorem of Morita, which leads to a great number of relations among tautological classes on moduli spaces of curves.
It is interesting to know, how far we can generalize the notion of a group-valued cocycle keeping the property to determine a bundle. We find a generalization for pairs of cocycles and show how these generalized pairs of cocycles can still…
We investigate linear relations among a class of iterated integrals on the Riemann sphere minus four points $0,1,z$ and $\infty$. Generalization of the duality formula and the sum formula for multiple zeta values to the iterated integrals…
Driven by a large number of potential applications in areas like bioinformatics, information retrieval and social network analysis, the problem setting of inferring relations between pairs of data objects has recently been investigated…
We give some inclusion relations for arbitrary fuzzy sets with reference to famous inequalities. In particular, we can know that the bounded sum and the algebraic product go well together. We would like to propose the concept of `Fuzzy Set…
For odd $k$, we give a formula for the relations between double zeta values $\zeta(r,k-r)$ with $r$ even. This formula provides a connection with the space of cusp forms on $\mathrm{SL}_2(\mathbb{Z})$. This is the odd weight analogue of a…
The goal of this article is to give an elementary proof of the double shuffle relations directly for the Goncharov and Manin motivic multiple zeta values. The shuffle relation is straightforward, but for the stuffle we use a modification of…
We study a class obtained from the Segre class $s(Z,Y)$ of an embedding of schemes by incorporating the datum of a line bundle on $Z$. This class satisfies basic properties analogous to the ordinary Segre class, but leads to remarkably…
The theory of finite automata applies to the study on relations of multiple zeta values.
We investigate relative holomorphic connections on a principal bundle over a family of compact complex manifolds. A sufficient condition is given for the existence of a relative holomorphic connection on a holomorphic principal bundle over…
In this paper we consider a family of multiple Hurwitz zeta values with bi-indices parameterized by $\mu$ with $\Ree(\mu)>0$. These values are equipped with both the $\mu$-stuffle product from their series definition and the shuffle product…
This paper develops a generalized cotangent-type series, extending classical expansions to higher-order lattice sums. By introducing a new family of series indexed by integer powers, we derive closed form representations that combine…
We study generating functions for multiple zeta star values in general form. These generating functions provide a connection between multiple zeta star values and multiple Euler sums, which allows us to express each multiple zeta star value…
The notion of cellular stratified spaces was introduced in a joint work of the author with Basabe, Gonz{\'a}lez, and Rudyak with the aim of constructing a cellular model of the configuration space of a sphere. Although the original aim was…