Integer-valued definable functions
Integer-valued definable functions
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2012
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Bulletin of the London Mathematical Society ; 44 (2012), 6. - pp. 1285-1291. - ISSN 0024-6093. - eISSN 1469-2120
Abstract
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 definable, analytic function f : [0,∞)k → |R is such that f(|N^k) ⊆ |Z, then either sup|¯x| <= r |f(¯x)| grows faster
than exp(rδ), for some δ > 0, or f is a polynomial over Q.
than exp(rδ), for some δ > 0, or f is a polynomial over Q.
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Subject (DDC)
510 Mathematics
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Reell-analytische Funktionen,O-Minimalität
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JONES, Gareth O., Margaret E. M. THOMAS, Alex J. WILKIE, 2012. Integer-valued definable functions. In: Bulletin of the London Mathematical Society. 44(6), pp. 1285-1291. ISSN 0024-6093. eISSN 1469-2120. Available under: doi: 10.1112/blms/bds059BibTex
@article{Jones2012Integ-20448, year={2012}, doi={10.1112/blms/bds059}, title={Integer-valued definable functions}, number={6}, volume={44}, issn={0024-6093}, journal={Bulletin of the London Mathematical Society}, pages={1285--1291}, author={Jones, Gareth O. and Thomas, Margaret E. M. and Wilkie, Alex J.} }
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