Integer points on the dilation of a subanalytic surface

@article{Pila2004IntegerPO,
  title={Integer points on the dilation of a subanalytic surface},
  author={J. Pila},
  journal={Quarterly Journal of Mathematics},
  year={2004},
  volume={55},
  pages={207-223}
}
  • J. Pila
  • Published 2004
  • Mathematics
  • Quarterly Journal of Mathematics
Let � ⊂ R n be a compact subanalytic set of dimension 2 and t 1. This paper gives an upper bound as t →∞ for the number of integer points on the homothetic dilation tofthat do not reside on any connected semialgebraic subset of tof positive dimension. Implications for the density of rational points onare also elaborated. 
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References

SHOWING 1-10 OF 14 REFERENCES
Integer points on hypersurfaces
Integer points on curves and surfaces
Geometric postulation of a smooth function and the number of rational points
The number of integral points on arcs and ovals
OSCILLATION OF ANALYTIC CURVES
An asymptotic expression for the number of solutions of a general class of Diophantine equations
Number Theory III: Diophantine Geometry
...
1
2
...