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Counting rational points on a certain exponential-algebraic surface

Jonathan Pila — 2010

Annales de l’institut Fourier

We study the distribution of rational points on a certain exponential-algebraic surface and we prove, for this surface, a conjecture of A. J. Wilkie.

The density of rational points on a pfaff curve

Jonathan Pila — 2007

Annales de la faculté des sciences de Toulouse Mathématiques

This paper is concerned with the density of rational points on the graph of a non-algebraic pfaffian function.

Rational points on a subanalytic surface

Jonathan Pila — 2005

Annales de l’institut Fourier

Let $X \subset ℝ^{n}$ be a compact subanalytic surface. This paper shows that, in a suitable sense, there are very few rational points of $X$ that do not lie on some connected semialgebraic curve contained in $X$ .

Concordant sequences and integral-valued entire functions

Jonathan Pila; Fernando Rodriguez Villegas — 1999

Acta Arithmetica

A classic theorem of Pólya shows that the function $2^{z}$ is the “smallest” integral-valued entire transcendental function. A variant due to Gel’fond applies to entire functions taking integral values on a geometric progression of integers, and Bézivin has given a generalization of both results. We give a sharp formulation of Bézivin’s result together with a further generalization.

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Currently displaying 1 – 4 of 4

Counting rational points on a certain exponential-algebraic surface

The density of rational points on a pfaff curve

Rational points on a subanalytic surface

Concordant sequences and integral-valued entire functions