Related papers: Special relations between multizeta values and par…
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…
In this paper, we explain several conjectures about how a product of two Carlitz-Goss zeta values can be expressed as a F_p-linear combination of Thakur's multizeta values, generalizing the q=2 case dealt by D. Thakur in Relations between…
Multizeta values in positive characteristic were first introduced and studied by Thakur. He and Lara Rodr\'{\i}guez discovered and conjectured certain zeta-like families. Kuan and Lin stated more conjectures about zeta-like multizeta…
We prove and conjecture several relations between multizeta values for $\mathbb{F}_q[t]$, focusing on zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or equivalently algebraic). In particular,…
In this paper, we study multiple zeta values (abbreviated as MZV's) over function fields in positive characteristic. Our main result is to prove Thakur's basis conjecture, which plays the analogue of Hoffman's basis conjecture for real…
Multiples zeta values and alternating multiple zeta values in positive characteristic were introduced by Thakur and Harada as analogues of classical multiple zeta values of Euler and Euler sums. In this paper we determine all linear…
The special values of multiple polylogarithms, which including multiple zeta values, appear some fields of mathematics and physics. Many kinds of their linear relations are investigated as well as their algebraic relations. From the…
In this paper, we give a formula that connects two variants of multiple zeta values; multitangent functions and symmetric multiple zeta values. As an application of this formula, we give two results. First, we prove Bouillot's conjecture on…
We prove or conjecture several relations between the multizeta values for positive genus function fields of class number one, focusing on the zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or…
We introduce alternating multizeta values in positive characteristic which are generalizations of Thakur multizeta values. We establish their fundamental properties including non-vanishing, sum-shuffle relations, period interpretation and…
This paper discusses four formulae conjectured by J. A. Lara Rodr\'iguez on certain power series in function fields, which yield a 'harmonic product' formula for Thakur's double zeta values. We prove affirmatively the first two formulae.…
We give an explicit formula for the well-known parity result for multiple zeta values as an application of the multitangent functions.
We prove a sum-shuffle formula for multiple zeta values in Tate algebras (in positive characteristic), introduced in \cite{PEL3}.This follows from an analog result for double twisted power sums, implying that an ${\mathbb{F}\_p$-vector…
In this note, we shall discuss a generalization of Thakur's multiple zeta values and allied objects, in the framework of function fields of positive characteristic and more precisely, of periods in Tate algebras.
Thakur (2010) showed that, for $r,$ $s\in \mathbb{N}$, a product of two Carlitz zeta values $\zeta_A(r)$ and $\zeta_A(s)$ can be expressed as an $\mathbb{F}_p$-linear combination of $\zeta_A(r+s)$ and double zeta values of weight $r+s$.…
We study trivial multiple zeta values in Tate algebras. These are particular examples of the multiple zeta values in Tate algebras in positive characteristic introduced by the second author. If the number of variables involved is 'not…
Many $\mathbb{Q}$-linear relations exist between multiple zeta values, the most interesting of which are various weighted sum formulas. In this paper, we generalized these to Euler sums and some other variants of multiple zeta values by…
The sum formula is one of the most well-known relations among multiple zeta values. This paper proves a conjecture of Kaneko predicting that an analogous formula holds for finite multiple zeta values.
We provide a period interpretation for multizeta values (in the function field context) in terms of explicit iterated extensions of tensor powers of Carlitz motives (mixed Carlitz-Tate t-motives). We give examples of combinatorially…
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…