Counting special points: Logic, diophantine geometry, and transcendence theory

Scanlon, Thomas

doi:10.1090/S0273-0979-2011-01354-4

Counting special points: Logic, diophantine geometry, and transcendence theory
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Bull. Amer. Math. Soc. 49 (2012), 51-71 Request permission

Abstract:

We expose a theorem of Pila and Wilkie on counting rational points in sets definable in o-minimal structures and some applications of this theorem to problems in diophantine geometry due to Masser, Peterzil, Pila, Starchenko, and Zannier.

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