Related papers: Motivic interpretations for iterated integrals on …
We introduce an iterated integral version of (generalized) log-sine integrals (iterated log-sine integrals) and prove a relation between a multiple polylogarithm and iterated log-sine integrals. We also give a new method for obtaining…
The MZV algebra is the graded algebra over ${\bold Q}$ generated by all multiple zeta values. The stable derivation algebra is a graded Lie algebra version of the Grothendieck-Teichm\"{u}ller group. We shall show that there is a canonical…
A well-known conjecture of Gross and Zagier states that the values of the higher automorphic Green's function at pairs of points with complex multiplication in the upper half-plane are proportional to the logarithm of an algebraic number.…
The zeta function of a motive over a finite field is multiplicative with respect to the direct sum of motives. It has beautiful analytic properties, as were predicted by the Weil conjectures. There is also a multiplicative zeta function,…
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…
Deligne and Goncharov constructed a neutral tannakian category of mixed Tate motives unramified over $\mathbb{Z}[\mu_N,1/N]$. Brown and Hain--Matsumoto computed the depth 2 quadratic relations of the motivic Galois group of this category…
In this paper, we construct four different theories of integration, two that are for Voevodsky motives, one for mixed $\ell$-adic sheaves, and a fourth theory of integration for rational mixed Hodge structures. We then show that they…
With representation-theoretic applications in mind, we construct a formalism of reduced motives with integral coefficients. These are motivic sheaves from which the higher motivic cohomology of the base scheme has been removed. We show that…
In this paper we shall define the renormalization of the multiple $q$-zeta values (M$q$ZV) which are special values of multiple $q$-zeta functions $\zeta_q(s_1,...,s_d)$ when the arguments are all positive integers or all non-positive…
In this paper we present some new identities for multiple polylogarithms (abbr. MPLs) and multiple harmonic star sums (abbr. MHSSs) by using the methods of iterated integral computations of logarithm functions. Then, by applying these…
This is the second installment in a sequence of articles devoted to "explicit Chabauty-Kim theory" for the thrice punctured line. Its ultimate goal is to construct an algorithmic solution to the unit equation whose halting will be…
The appearance of multiple zeta values in anomalous dimensions and $\beta$-functions of renormalizable quantum field theories has given evidence towards a motivic interpretation of these renormalization group functions. In this paper we…
We extend the block filtration, defined by Brown based on the work of Charlton, to all motivic multiple zeta values, and study relations compatible with this filtration. We construct a Lie algebra describing relations among motivic multiple…
The motivic coaction of multiple zeta values and multiple polylogarithms encodes both structural insights on and computational methods for scattering amplitudes in a variety of quantum field theories and in string theory. In this work, we…
We define finite multiple zeta values (FMZVs) associated with some combinatorial objects, which we call 2-colored rooted trees, and prove that FMZVs associated with 2-colored rooted trees satisfying certain mild assumptions can be written…
We give an evaluation for the stuffle-regularised $t^{\ast,V}(\{2\}^a,1,\{2\}^b)$ as a polynomial in single-zeta values, $\log(2)$ and $V$. We then apply this to establish some linear independence results of certain sets of motivic multiple…
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.
We confirm a conjecture about the construction of basis elements for the multiple zeta values (MZVs) at weight 27 and weight 28. Both show as expected one element that is twofold extended. This is done with some lengthy computer algebra…
We define a divisorial motivic zeta function for stable curves with marked points which agrees with Kapranov's motivic zeta function when the curve is smooth and unmarked. We show that this zeta function is rational, and give a formula in…
The algebra of big zeta values we introduce in this paper is an intermediate object between multiple zeta values and periods of the multiple zeta motive. It consists of number series generalizing multiple zeta values, the simplest examples,…