Integer-valued definable functions
نویسندگان
چکیده
We present a dichotomy, in terms of growth at infinity, of analytic functions definable in the real exponential field which take integer values at natural number inputs. Using a result concerning the density of rational points on curves definable in this structure, we show that if a function f : [0,∞) → R is such that f(N) ⊆ Z, then either sup|x̄|≤r f(x̄) grows faster than exp(r), for some δ > 0, or f is a polynomial over Q.
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