Submission date: 18 May 2020

Abstract:

We give two variations on a result of Wilkie's on unary functions definable in ℝ_{an,exp} that take integer values at positive integers. Provided that the functions grows slower than the function 2^x, Wilkie showed that is must be eventually equal to a polynomial. We show the same conclusion under a stronger growth condition but only assuming that the function takes values sufficiently close to a integers at positive integers. In a different variation we show that it suffices to assume that the function takes integer values on a sufficiently dense subset of the positive integers(for instance primes), again under a stronger growth bound than that in Wilkie's result.

Mathematics Subject Classification:

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Full text arXiv 2005.08852: pdf, ps.