Note on the rational points of a pfaff curve

2005/06/15 by Jonathan Pila, Pila, Jonathan
Mathematics · #11D99 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D99

paper · pdf · doi:10.48550/arxiv.math/0506293

8 pages

arxiv created 2005/06/15 · arxiv updated 2009/12/01

Abstract

Let X be the graph in the plane of a pfaffian function f (in the sense of Khovanskii). Suppose X is not algebraic. This note gives an upper bound for the number of rational points on X of height up to X. The bound is uniform in the order and degre of f.

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