Home | Quick Search | Advanced Search | Bibliography submission | Bibliography submission using bibtex | Bibliography submission using bibtex file | Links | Help | Internal

# 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 y-directions, and we also estimate integer points close to the curve, with \left|n - 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 0208-6573 URL http://projecteuclid.org/euclid.facm/1229618752 Language English Journal Funct. Approximatio, Comment. Math. Volume 37 Pages 213--231 Publisher Uniwersytet Im. Adama Mickiewicza (UAM), Pozn Year 2007 Edition 0 Translation No Refereed No
Webmaster