Add to ORKGWe establish a rigid-analytic analog of the Pila-Wilkie counting theorem, giving sub-polynomial upper bounds for the number of rational points in the transcendental part of a $\mathbb{Q}_p$-analytic set, and the number of rational functions in a $\mathbb{F}_q((t))$-analytic set. For $\mathbb{Z}[[t]]$-analytic sets we prove such bounds uniformly for the specialization to every non-archimedean local field
In this thesis I study various incarnations of rational homotopy theory in the world of arithmetic g...
The ring of polynomials over a finite field has many arithmetic properties similar to those of the r...
Let $P\in\mathbb{P}_1(\mathbb{Q})$ be a periodic point for a monic polynomial with coefficients in $...
Let $K\subseteq \mathbb{R}$ be a number field. Using techniques of discrete analysis, we prove that ...
This expository paper gives an account of the Pila-Wilkie counting theorem and some of its extension...
We construct families of curves which provide counterexamples for a uniform boundedness question. ...
Consider the vanishing locus of a real analytic function on $\mathbb{R}^n$ restricted to $[0,1]^n$. ...
This thesis concerns the study of the density of rational and algebraic points in the transcendental...
We consider the problem of counting the number of varieties in a family over $\mathbb{Q}$ with a rat...
We carry out an arithmetical study of analytic functions f:[0,1]→[0,1] that by restriction induce a ...
We prove new parameterization theorems for sets definable in the structure ℝan (i.e. for globally su...
Contains fulltext : 162943.pdf (publisher's version ) (Closed access
In this note, we give an alternative proof of uniform boundedness of the number of integral points o...
An upper bound sieve for rational points on suitable varieties isdeveloped, together with applicatio...
We prove some instances of Wilkie's conjecture on the density of rational points on sets definable i...
In this thesis I study various incarnations of rational homotopy theory in the world of arithmetic g...
The ring of polynomials over a finite field has many arithmetic properties similar to those of the r...
Let $P\in\mathbb{P}_1(\mathbb{Q})$ be a periodic point for a monic polynomial with coefficients in $...
Let $K\subseteq \mathbb{R}$ be a number field. Using techniques of discrete analysis, we prove that ...
This expository paper gives an account of the Pila-Wilkie counting theorem and some of its extension...
We construct families of curves which provide counterexamples for a uniform boundedness question. ...
Consider the vanishing locus of a real analytic function on $\mathbb{R}^n$ restricted to $[0,1]^n$. ...
This thesis concerns the study of the density of rational and algebraic points in the transcendental...
We consider the problem of counting the number of varieties in a family over $\mathbb{Q}$ with a rat...
We carry out an arithmetical study of analytic functions f:[0,1]→[0,1] that by restriction induce a ...
We prove new parameterization theorems for sets definable in the structure ℝan (i.e. for globally su...
Contains fulltext : 162943.pdf (publisher's version ) (Closed access
In this note, we give an alternative proof of uniform boundedness of the number of integral points o...
An upper bound sieve for rational points on suitable varieties isdeveloped, together with applicatio...
We prove some instances of Wilkie's conjecture on the density of rational points on sets definable i...
In this thesis I study various incarnations of rational homotopy theory in the world of arithmetic g...
The ring of polynomials over a finite field has many arithmetic properties similar to those of the r...
Let $P\in\mathbb{P}_1(\mathbb{Q})$ be a periodic point for a monic polynomial with coefficients in $...