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Rational points on a subanalytic surface

Jonathan Pila — 2005

Annales de l’institut Fourier

Let X 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 PilaFernando 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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