Related papers: An algebraic integration for Mahler measure

In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…

Motivated by a famous question of Lehmer about the Mahler measure we study and solve its analytic analogue.

In this note, we show how the penalization method, introduced in order to describe some non-trivial changes of the Wiener measure, can be applied to the study of some simple polymer models such as the pinning model. The bulk of the analysis…

Let $M(\alpha)$ denote the Mahler measure of the algebraic number $\alpha$. In a recent paper, Dubickas and Smyth constructed a metric version of the Mahler measure on the multiplicative group of algebraic numbers. Later, Fili and the…

It is known that multiple zeta values can be written in terms of certain iterated log-sine integrals. Conversely, we evaluate iterated log-sine integrals in terms of multiple polylogarithms and multiple zeta values in this paper. We also…

The paper presents a survey over frame multipliers and related concepts. In particular, it includes a short motivation of why multipliers are of interest to consider, a review as well as extension of recent results, devoted to the…

Let $\chi_{-f}$ be the odd quadratic Dirichlet character of conductor $f$, and let $\mathrm{m}(P)$ denote the Mahler measure of a polynomial $P$. In 1984, Chinburg conjectured that for any such $\chi_{-f}$ there exist an integral bivariate…

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…

Let $T$ be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over $T$, one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in…

The hyper-Mahler measures $m_k( 1+x_1+x_2),k\in\mathbb Z_{>1}$ and $m_k( 1+x_1+x_2+x_3),k\in\mathbb Z_{>1}$ are evaluated in closed form via Goncharov-Deligne periods, namely $\mathbb Q$-linear combinations of multiple polylogarithms at…

We show that for almost every polynomial P(x,y) with complex coefficients, the difference of the logarithmic Mahler measures of P(x,y) and P(x,x^n) can be expanded in a type of formal series similar to an asymptotic power series expansion…

Matrix valued Laguerre polynomials are introduced via a matrix weight function involving several degrees of freedom using the matrix nature. Under suitable conditions on the parameters the matrix weight function satisfies matrix Pearson…

In our present investigation we propose to study and develop the I-function of two variables analogous to the I-function of one variable introduced and studied by one of the authors[24]. The conditions for convergence, series…

Building upon earlier work in which axioms were formulated for multivariate measures of concordance, we examine properties of such measures. In particular, we examine the relations between the measure of concordance of an $n$-copula and the…

We develop a new approach to the study of the functional equations satisfied by classical polylogarithms, inspired by Goncharov's conjectures. We prove a sharpened version of Zagier's criterion for such an equation and explain, how our…

We prove a conjecture of Boyd and Rodriguez Villegas relating the Mahler measure of the polynomial $(1+x)(1+y)+z$ and the value at $s=3$ of the $L$-function of an elliptic curve of conductor $15$. The proof makes use of the computation by…

With assumption that an optical element is described by a Mueller matrix of the Lorentzian type, a method to find a 3-dimensional complex vector parameter for a corresponding Mueller matrix from results of four specially chosen polarization…

We present necessary and sufficient conditions for the existence of a countably additive measure on a complete Boolean algebra.

Feynman integrals are very often computed from their differential equations. It is not uncommon that the $\varepsilon$-factorised differential equation contains only dlog-forms with algebraic arguments, where the algebraic part is given by…

This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…