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Integer-valued definable functions.
- Source :
-
Bulletin of the London Mathematical Society . Dec2012, Vol. 44 Issue 6, p1285-1291. 7p. - Publication Year :
- 2012
-
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(ℕk) ⊆ ℤ, then either sup|x̄|≤ r |f(x̄)| grows faster than exp(rδ), for some δ>0, or f is a polynomial over ℚ. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00246093
- Volume :
- 44
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Bulletin of the London Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 83745969
- Full Text :
- https://doi.org/10.1112/blms/bds059