Submission date: 12 January 2016.

Abstract:

We show that transcendental curves in $R^n$ (not necessarily compact) have few rational points of bounded height provided that the curves are well behaved with respect to algebraic sets and can be parametrized by functions belonging to a specified algebra of infinitely differentiable functions. The method is based on that of Bombieri and Pila, and extends to the non-o-minimal setting some earlier results by others on Pfaffian curves and special functions.

Mathematics Subject Classification:

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Full text arXiv 1601.03033: pdf, ps.