2012.1: Integer-valued definable functions
2012.1: A J Wilkie, G O Jones and M E M Thomas (2012) Integer-valued definable functions.
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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;1)n ! R is such that f(Nn) Z, then either supjxjr f(x) grows faster than exp(r), for some > 0, or f is a polynomial over Q.
|Item Type:||MIMS Preprint|
|Uncontrolled Keywords:||O-minimality, number theory, CICADA|
|Subjects:||MSC 2000 > 03 Mathematical logic and foundations|
MSC 2000 > 11 Number theory
MSC 2000 > 26 Real functions
|Deposited By:||Prof Alex J Wilkie|
|Deposited On:||05 January 2012|