Related papers: On finite Carlitz multiple polylogarithms

Pellarin introduced the deformation of multiple zeta values of Thakur as elements over Tate algebras. In this paper, we relate these values to a certain coordinate of a higher dimensional Drinfeld module over Tate algebras which we will…

We prove that the category of mixed Tate motives over $\Z$ is spanned by the motivic fundamental group of $\Pro^1$ minus three points. We prove a conjecture by M. Hoffman which states that every multiple zeta value is a $\Q$-linear…

We generalize Carlitz' result on the number of self reciprocal monic irreducible polynomials over finite fields by showing that similar explicit formula hold for the number of irreducible polynomials obtained by a fixed quadratic…

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 $r+s$.…

In this paper, we study various twisted A-harmonic sums, named following the seminal log-algebraicity papers of G. Anderson. These objects are partial sums of new types of special zeta values introduced by the first author and linked to…

In this note we prove that for all $a \in \mathbb{N}$, $x \in \mathbb{R}_+ \cup \{0\}$, and $s \in \mathbb{C}$ with $\Re(s) > a + 2$, the (alternating) weighted series of the Hurwitz zeta function, $$ \sum_{k \geq 1} (\pm 1)^k (k +…

We study the set of common F_q-rational zeros of systems of multivariate symmetric polynomials with coefficients in a finite field F_q. We establish certain properties on these polynomials which imply that the corresponding set of zeros…

We provide a framework for relating certain q-series defined by sums over partitions to multiple zeta values. In particular, we introduce a space of polynomial functions on partitions for which the associated q-series are q-analogues of…

We describe a solution of the Gauss hypergeometric equation, $F(\alpha,\beta,\gamma;z)$ by power series in paramaters $\alpha,\beta,\gamma$ whose coefficients are $\Z$ linear combinations of multiple polylogarithms. And using the…

Alternating variants of multiple poly-Bernoulli numbers and finite multiple zeta values in characteristic 0 and p This paper consists of two parts: the characteristic 0 part and the characteristic p part. In characteristic 0 part, we…

In 2007, Papanikolas established that if Carlitz logarithms of algebraic functions are linearly independent over the rational function field, then they are algebraically independent. The purpose of the present paper is to provide a new…

Maximon has recently given an excellent summary of the properties of the Euler dilogarithm function and the frequently used generalizations of the dilogarithm, the most important among them being the polylogarithm function $Li_(z)$. The…

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 extend the definition of Boolean canalyzing functions to the canalyzing functions over finite field $\mathbb{F}_{q}$, where $q$ is a power of a prime. We obtain the characterization of all the eight classes of such…

We use visible point vector identities to examine polylogarithms in the neighbourhood of the Riemann zeta function zeroes. New formulas limiting to the trivial zeroes and to the critical line on the zeta function are given. Similar results…

In this paper we develop the analytic theory of a multiple zeta function in d independent complex variables defined over a global function field. This is the function field analog of the Euler-Zagier multiple zeta function of depth d.

In this sequel to our recent note it is shown, in a unified manner, by making use of some basic properties of certain special functions, such as the Hurwitz zeta function, Lerch zeta function and Legendre chi function, that the values of…

Let $\mathfrak{p}$ be a monic irreducible polynomial in $A:=\mathbb{F}_q[\theta]$, the ring of polynomials in the indeterminate $\theta$ over the finite field $\mathbb{F}_q$, and let $\zeta$ be a root of $\mathfrak{p}$ in an algebraic…

Finite hypergeometric functions are complex valued functions on finite fields which are the analogue of the classical analytic hypergeometric functions. From the work of N.M.Katz it follows that their values are traces of Frobenius on…

We prove a multiplication theorem for quantum cluster algebras of acyclic quivers. The theorem generalizes the multiplication formula for quantum cluster variables in \cite{fanqin}. We apply the formula to construct some $\mathbb{ZP}$-bases…