Related papers: Ap\'ery limits and Mahler measures
We prove that certain sequences of Laurent polynomials, obtained from a fixed Laurent polynomial P by monomial substitutions, give rise to sequences of Mahler measures which converge to the Mahler measure of P. This generalizes previous…
This is the first part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. We prove two main results concerning systems that are regular singular at…
A Thesis about Euler discussing the possibilities and limits of his method of work in Mathematics.
The Annals of Applied Probability (2002) 12 1114-1137
The work studies some Difference equations, which are connected with Mejer's function.
We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.
In the following paper a version of the classical Mahler formula is found. The height and the measure are now relative to a self-map on a projective space of arbitrary dimension.
This is an introductory article to the theory of multiple gaps.
We consider upper and lower bounds on the minimal height of an irrational number lying in a particular real quadratic field.
Recent work of Pritsker defines and studies an areal version of the Mahler measure. We further explore this function with a particular focus on the case where its value is small, as this is most relevant to Lehmer's conjecture. In this…
Mahler's measure defines a dynamical system on the algebraic numbers. In this paper, we study the problem of which number fields have points which wander under the iteration of Mahler's measure. We completely solve the problem for all…
Kurokawa, Lal\'{\i}n and Ochiai introduced and studied the higher Mahler measures, which are generalization of the classical Mahler measure. In this article, we introduce $p$-adic higher Mahler measures and prove $p$-adic analogues of…
Here we give a lower bound of the Mahler measure on a set of polynomials that are "almost" reciprocal. Here "almost" reciprocal means that the outermost coefficients of each polynomial mirror each other in proportion, while this pattern…
The Mahler measures of certain polynomials of up to five variables are given in terms of multiple polylogarithms. Each formula is homogeneous and its weight coincides with the number of variables of the corresponding polynomial.
Paper withdrawn, see math-ph/0505072
The metric Mahler measure was first studied by Dubickas and Smyth in 2001 as a means of phrasing Lehmer's conjecture in topological language. More recent work of the author examined a parametrized family of generalized metric Mahler…
Adopting the Mahler measure from number theory, we introduce it to toric quiver gauge theories, and study some of its salient features and physical implications. We propose that the Mahler measure is a universal measure for the quiver,…
This note is an addendum to the paper ''Mahler's method in several variables and finite automata''. It strengthens part (i) of Theorem 1.1 of the aforementioned paper.
Mahler has written many papers on the geometry of numbers. Arguably, his most influential achievements in this area are his compactness theorem for lattices, his work on star bodies and their critical lattices, and his estimates for the…
For an (irreducible) recurrence equation with coefficients from $\mathbb Z[n]$ and its two linearly independent rational solutions $u_n,v_n$, the limit of $u_n/v_n$ as $n\to\infty$, when exists, is called the Ap\'ery limit. We give a…