This article introduces an algebra $\mathscr{A}_{\mathsf{MTV}, c}$ of functions in one variable $c$ defined by iterated integrals two specific differential forms depending on $c$, where the product is shuffle product. The can be seen as a common deformation multiple zeta values and Kaneko-Tsumura's recent $T$-values it satisfies same duality relations. Its first graded dimensions, assuming that...

Historically the polylogarithm has attracted specialists and non specialists alike with its lovely evaluations Much the same can be said for Euler sums or multiple harmonic sums which within the past decade have arisen in combinatorics knot theory and high energy physics More recently we have been forced to consider multidimensional extensions encompassing the classical polylogarithm Euler sums...

We study some classical identities for multiple zeta values and show that they still hold functions built from an arbitrary sequence of nonzero complex numbers. introduce the complementary function a system, which naturally occurs when lifting to quasisymmetric functions.

We build, using the notion of zinbiel algebra, some commutative subalgebras C_{u,v} inside an algebra formal iterated integrals. There is a quotient map from this integrals to motivic multiple zeta values. Restricting gives morphism graded algebras with same dimension. This conjectured be generically isomorphism. When u+v = 0, image instead sub-algebra