Integer-valued definable functions

Jones, Gareth O.; Thomas, Margaret E. M.; Wilkie, Alex J.

Integer-valued definable functions

Files

Integer-valued definable functions.pdf(505.39 KB)

Date

2012

Authors

Jones, Gareth O.

Thomas, Margaret E. M.

Wilkie, Alex J.

Publication type

Journal article

Published in

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(r^δ), for some δ > 0, or f is a polynomial over Q.

Subject (DDC)

510 Mathematics

Keywords

Reell-analytische Funktionen,O-Minimalität

Cite This

ISO 690

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/bds059

BibTex

@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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Yes