Related papers: Ap\'ery limits and Mahler measures
We describe a general method to determine the Apery limits of a differential equation that have a modular-function origin. As a by-product of our analysis, we discover a family of identities involving the special values of L-functions…
This article investigates the Mahler measure of a family of 2-variate polynomials, denoted by $P_d, d\geq 1$, unbounded in both degree and genus. By using a closed formula for the Mahler measure introduced in "Volume function and Mahler…
We consider some critical claims concerning our above paper, and reply to these claims.
We address the Mach limit problem for the Euler equations in the analytic spaces. We prove that, given analytic data, the solutions to the compressible Euler equations are uniformly bounded in a suitable analytic norm and then show that the…
In a previous paper, the authors introduced several vector space norms on the space of algebraic numbers modulo torsion which corresponded to the Mahler measure on a certain class of numbers and allowed the authors to formulate L^p Lehmer…
This is an expository article, closely following the author's lecture at the 2014 Journal Differential Geometry conference.
This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
Using twistor methods we derive a generating function which leads to the hyperk\" ahler metric on a deformation of the Atiyah-Hitchin monopole moduli space. This deformation was first considered by Dancer through the quotient construction…
We lay foundations of the subject in the title, on which we build in another paper devoted to isometries in spaces of K\"ahler metrics.
In this paper, we first prove a folklore conjecture on a greatest lower bound of the Calabi energy in all K\"ahler manifold. Similar result in algebriac setting was obtained by S. K. Donaldson. Secondly, we give an upper/lower bound…
We study the distribution of primes from a topological viewpoint. Certain conjecture is introduced, and we show that it is equivalent to the Riemann Hypothesis.
We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. The dynamics for arities of…
In this article we study limits of models that contain a dimensionful parameter such as the mass of the relativistic point-particle. The limits are analogous to the massless limit of the particle and may be thought of as high energy limits.…
In recent years some near-optimal estimates have been established for certain sum-product type estimates. This paper gives some first extremal results which provide information about when these bounds may or may not be tight. The main tool…
This paper is devoted to the study of the low Mach number limit for the 2D isentropic Euler system associated to ill-prepared initial data with slow blow up rate on $\log\varepsilon^{-1}$. We prove in particular the strong convergence to…
Here we propose a survey on Mahler's theory for transcendence and algebraic independence focusing on certain applications to the arithmetic of periods of Anderson t-motives.
We present an exact formula for the Mahler measure of an infinite family of polynomials with arbitrarily many variables. The formula is obtained by manipulating the integral defining the Mahler measure using certain transformations,…
Let f be a dominating meromorphic self-map of large topological degree on a compact Kaehler manifold. We give a new construction of the equilibrium measure of f and prove that it is exponentially mixing. Then, we deduce the central limit…