Details:
Title  The integer points in a plane curve.  Author(s)  Martin N. Huxley  Type  Article in Journal  Abstract  Bombieri and Pila gave sharp estimates for the number of integer points (m,n) on a given arc of a curve y=F(x), enlarged by some size parameter M, for algebraic curves and for transcendental analytic curves. The transcendental case involves the maximum number of intersections of the given arc by algebraic curves of bounded degree. We obtain an analogous result for functions F(x) of some class Ck that satisfy certain differential inequalities that control the intersection number. We allow enlargement by different size parameters M and N in the x and ydirections, and we also estimate integer points close to the curve, with
\leftn  NF ( {m\over M} ) \leq \delta,
for δ sufficiently small in terms of M and N. As an appendix we obtain a determinant mean value theorem which is a quantitative version of a linear independence theorem of Pólya.  ISSN  02086573 
URL 
http://projecteuclid.org/euclid.facm/1229618752 
Language  English  Journal  Funct. Approximatio, Comment. Math.  Volume  37  Pages  213231  Publisher  Uniwersytet Im. Adama Mickiewicza (UAM), Pozn  Year  2007  Edition  0  Translation 
No  Refereed 
No 
