Related papers: Ap\'ery limits and Mahler measures

The paper is devoted to the properties of the Lagrange spectrum left endpoints and so-called attainable numbers.

The "Mahler volume" is, intuitively speaking, a measure of how "round" a centrally symmetric convex body is. In one direction this intuition is given weight by a result of Santalo, who in the 1940s showed that the Mahler volume is…

Let $M(\alpha)$ denote the (logarithmic) Mahler measure of the algebraic number $\alpha$. Dubickas and Smyth, and later Fili and the author, examined metric versions of $M$. The author generalized these constructions in order to associate,…

This note provides examples of all possible equality and strict inequality relations between upper and lower Abelian and Cesaro limits of sequences bounded above or below.

We consider the low Mach number limit problem of the Euler equations for isentropic fluids in the analytic spaces. We prove that, given general analytic initial data, the solution is uniformly bounded on a time interval independent of the…

This is a short review on the applications of Lieb-Robinson bounds for a general readership of mathematical physicists.

In this note we provide a new, algebraic proof of the excessive Laurent phenomenon for mutations of potentials (in the sense of [Galkin S., Usnich A., Preprint IPMU 10-0100, 2010]) by introducing to this theory the analogue of the upper…

An important component of Ap\'ery's proof that $\zeta (3)$ is irrational involves representing $\zeta (3)$ as the limit of the quotient of two rational solutions to a three-term recurrence. We present various approaches to such Ap\'ery…

We provide a new cohomological obstruction to the existence of astheno-Kahler metrics, and study relevant examples.

Answering a problem of Eklof and Mekler, we show that there is a reflexive group of cardinality >= first measurable.

An elementary proof of Kepler's first law, i.e. that bounded planetary orbits are elliptical, is derived without the use of calculus. The proof is similar in spirit to previous derivations, in that conservation laws are used to obtain an…

This paper gives a short introduction into the metric theory of spaces with dilations.

The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.

Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler conjecture {\mf for symmetric convex bodies}. Our contributions include, in particular, simple self-contained proofs of their two key statements.…

The paper deals with locally bounded solutions of a Schilling's problem.

We obtain new lower and upper bounds for probabilities of unions of events.These bounds are sharp. They are stronger than earlier ones. General bounds maybe applied in arbitrary measurable spaces.We have improved the method that has been…

We discuss how metric limits and rescalings of K\"ahler-Einstein metrics connect with Algebraic Geometry, mostly in relation to the study of moduli spaces of varieties, and singularities. Along the way, we describe some elementary examples,…

We give an elementary introduction to hyperk\"ahler manifolds, survey some of their interesting properties and some open problems.

The paper is an introduction to intuitionistic mathematics.

This paper exploits adjacencies between the orbits of an ordered set P and a consequence of the classification of finite simple groups to, in many cases, exponentially bound the number of automorphisms. Results clearly identify the…