Related papers: Density of integral points on algebraic varieties

We derive some estimates for the integral modulus of continuity of probability densities of infinitely divisible distributions. The paper is splitted into two parts. The first part deals with general infinitely divisible distributions. The…

The distribution of rational points of bounded height on algebraic varieties is far from uniform. Indeed the points tend to accumulate on thin subsets which are images of non-trivial finite morphisms. The problem is to find a way to…

We estabilish some connections among the Makar-Limanov invariant, the Derksen invariant, and the existence of flexible points on an affine variety.

In a previous paper {GN2} an effective solution of the lattice point counting problem in general domains in semisimple S-algebraic groups and affine symmetric varieties was established. The method relies on the mean ergodic theorem for the…

We compute K-semistable domains for various examples of log pairs.

We discuss the probability distributions of Fourier modes of cosmological density fields using the central limit theorem as it applies to weighted integrals of random fields. It is shown that if the cosmological principle holds in a certain…

We survey results on the distribution of zeros of random polynomials and of random holomorphic sections of line bundles, especially for large classes of probability measures on the spaces of holomorphic sections. We provide furthermore some…

This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…

We prove that the local height of a point on a Drinfeld module can be computed by averaging the logarithm of the distance to that point over the torsion points of the module. This gives rise to a Drinfeld module analog of a weak version of…

We study algebraic points of bounded degree on polarized projective varieties. To do so, we refine further the filtration construction and Subspace Theorem approach, for the study of integral points, which has origins in the work of…

We study finite morphisms of varieties and the link between their top multiplicity loci under certain assumptions. More precisely, we focus on how to determine that link in terms of the spaces of arcs of the varieties.

We import ideas from geometry to settle Sarnak's saturation problem for a large class of algebraic varieties.

In this note, we consider applications of Ratner's theorem to constructions of families of polynomials with dense values on the set of primitive integer points from the viewpoint of invariant theory.

We solve a Lehmer-type question about the Mahler measure of integer-valued polynomials.

For a toric log variety with standard coefficients, we show that the minimal log discrepancy at a closed invariant point bounds the Cartier index of a neighbourhood.

A short note on bounds on distance to variety of a point in terms of the Taylor coefficients at the point.

We study automorphisms, isomorphisms, and derivations of the incidence algebra $I(X,R)$, where $X$ is preordered set and $R$ is an algebra over some commutative ring $T$.

We show the asymptotic degree distribution of the typical vertex of a sparse inhomogeneous random intersection graph.

Length density is a recently introduced factorization invariant, assigned to each element $n$ of a cancellative commutative atomic semigroup $S$, that measures how far the set of factorization lengths of $n$ is from being a full interval.…

This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ideal-theoretic complete intersections and absolutely…