Related papers: Equidistribution quantitative des points de petite…

We consider smooth projective curves C/$\mathbb{F}$ over a finite field and their symmetric squares $C^{(2)}$. For a global function field $K/\mathbb{F}$, we study the $K$-rational points of $C^{(2)}$. We describe the adelic points of…

We extend Urban's construction of eigenvarieties for reductive groups $G$ such that $G(\mathbb{R})$ has discrete series to include characteristic $p$ points at the boundary of weight space. In order to perform this construction, we define a…

We classify generically transitive actions of semidirect products of an additive and a multiplicative group on the projective plane. Motivated by the program to study the distribution of rational points on del Pezzo surfaces (Manin's…

We apply a variant of the square-sieve to produce a uniform upper bound for the number of rational points of bounded height on a family of surfaces that admit a fibration over the projective line, whose general fibre is a hyperelliptic…

Finite frames can be viewed as mass points distributed in $N$-dimensional Euclidean space. As such they form a subclass of a larger and rich class of probability measures that we call probabilistic frames. We derive the basic properties of…

Given a place $\omega$ of a global function field $K$ over a finite field, with associated affine function ring $R_\omega$ and completion $K_\omega$, the aim of this paper is to give an effective joint equidistribution result for…

We establish an adelic version of Dirichlet's approximation theorem on spheres. Let $K$ be a number field, $E$ be a rigid adelic space over $K$ and $q\colon E\to K$ be a quadratic form. Let $v$ be a place of $K$ and $\alpha\in…

A generative probabilistic model for relational data consists of a family of probability distributions for relational structures over domains of different sizes. In most existing statistical relational learning (SRL) frameworks, these…

This work is motivated by problems on simultaneous Diophantine approximation on manifolds, namely, establishing Khintchine and Jarnik type theorems for submanifolds of R^n. These problems have attracted a lot of interest since Kleinbock and…

The purpose of this article is twofold. On the one hand, we prove asymptotic formulas for the quantitative distribution of rational points on any smooth non-split projective quadratic surface. We obtain the optimal error term for the real…

The main goal of this paper is to obtain optimal estimates on the speed of equidistribution of nilflows on higher step nilmanifolds. Under a Diophantine condition on the frequencies of the toral projection of the flow, we prove that for…

Let $K$ be a algebraically closed field of characteristic 0 that is complete with respect to a non-Archimedean absolute value. Let $\phi\in K(z)$ with $\textrm{deg}(\phi)\geq 2$. In this paper we establish uniform logarithmic…

Let E be an elliptic curve defined over a number field k. In this paper, we define the ``global discrepancy'' of a finite set Z of algebraic points on E which in a precise sense measures how far the set is from being adelically…

Given a toric metrized R-divisor on a toric variety over a global field, we give a formula for the essential minimum of the associated height function. Under suitable positivity conditions, we also give formulae for all the successive…

A Dirichlet $k$-partition of a domain is a collection of $k$ pairwise disjoint open subsets such that the sum of their first Laplace--Dirichlet eigenvalues is minimal. In this paper, we propose a new relaxation of the problem by introducing…

We study a class of semilinear elliptic equations on spaces of tempered ultradistributions of Beurling and Roumieu type. Assuming that the linear part of the equation is an elliptic pseudodifferential operator of infinite order with a…

Consider the smooth projective models C of curves y^2=f(x) with f(x) in Z[x] monic and separable of degree 2g+1. We prove that for g >= 3, a positive fraction of these have only one rational point, the point at infinity. We prove a lower…

The distribution of primes raising the level of even Galois representations of tetrahedral type is studied. Data are presented on primes $v\leq 10^8$ raising the level of $3$-adic even representations of various conductors. Based on the…

The purpose of this article is twofold: to prove a pointwise equidistribution theorem with an error rate for almost smooth functions, which strengthens the main result of Kleinbock, Shi and Weiss (2017); and to obtain a L\'evy-Khintchin…

The embedding of a torus into an inner form of PGL(2) defines an adelic toric period. A general version of Duke's theorem states that this period equidistributes as the discriminant of the splitting field tends to infinity. In this paper we…