Related papers: Mixed Tate Motives and Multiple Zeta Values

We study relations between the multizeta values for function fields introduced by D. Thakur. The product \zeta(a)\zeta(b) is a linear combination of multizeta values. For q=2, a full conjectural description of how the product of two zeta…

For a variety with a Whitney stratification by affine spaces, we study categories of motivic sheaves which are constant mixed Tate along the strata. We are particularly interested in those cases where the category of mixed Tate motives over…

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…

We prove that the algebra of p-adic multi-zeta values are contained in another algebra which is defined explicitly in terms of series.

We derive an explicit formula for the quasi--shuffle product satisfied by Schlesinger--Zudilin Multiple~$q$-Zeta Values, expressed in terms of partition data. To achieve this, we interpret Schlesinger--Zudilin Multiple~$q$-Zeta Values as…

We build, using the notion of zinbiel algebra, some commutative subalgebras $C_{u,v}$ inside an algebra of formal iterated integrals. There is a quotient map from this algebra of formal iterated integrals to the algebra of motivic multiple…

We give a new construction, based on categorical logic, of Nori's $\mathbb Q$-linear abelian category of mixed motives associated to a cohomology or homology functor with values in finite-dimensional vector spaces over $\mathbb Q$. This new…

We study some classical identities for multiple zeta values and show that they still hold for zeta functions built on the zeros of an arbitrary function. We introduce the complementary zeta function of a system, which naturally occurs when…

In this paper we give two idelic representations of the multiple zeta values - one using iterated integrals over the finite ideles and the other using iterated integrals over the idele class group. Each of the representations leads to a…

We introduce iterated beta integrals, a new class of iterated integrals on the universal abelian covering of the punctured projective line that unifies hyperlogarithms and classical beta integrals while preserving their fundamental…

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…

A natural place to study the Chow ring of the classifying space $BG$, for $G$ a linear algebraic group, is Voevodsky's triangulated category of motives, inside which Morel and Voevodsky, and Totaro have defined motives $M(BG)$ and…

In this article we shall survey some recent progress on the study of Ap\'ery-like sums which are multiple variable generalizations of the two sums Ap\'ery used in his famous proof of the irrationality of $\zeta(2)$ and $\zeta(3)$. We only…

For a composition $I$ whose first part exceeds 1, we can define the multiple $t$-value $t(I)$ as the sum of all the terms in the series for the multiple zeta value $\zeta(I)$ whose denominators are odd. In this paper we show that if $I$ is…

Inspired by a recent work of M. Nakasuji, O. Phuksuwan and Y. Yamasaki we combine interpolated multiple zeta values and Schur multiple zeta values into one object, which we call interpolated Schur multiple zeta values. Our main result will…

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…

We prove an evaluation for the stuffle-regularised multiple $t$ value $ t^{\ast,V}(\{\overline{1}\}^a, 1, \{\overline{1}\}^b) $ in terms of $ \log(2) $, $ \zeta(k) $ and $ \beta(k) $. This arises by evaluating the corresponding generating…

In this paper, we introduce multiple zeta dagger values and special values of Carlitz multiple dagger polylogarithms, and study their properties. In particular, using these values, we construct a non-trivial involution on a certain quotient…

This paper studies Artin-Tate motives over number rings. As a subcategory of geometric motives, the triangulated category of Artin-Tate motives DATM(S) is generated by motives of schemes that are finite over the base S. After establishing…

In this paper, we study the combinatorics of a subcomplex of the Bloch-Kriz cycle complex [4] used to construct the category of mixed Tate motives. The algebraic cycles we consider properly contain the subalgebra of cycles that correspond…