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Conference to the Memory of Anatoly Alekseevitch Karatsuba on Number theory and Applications
January 29, 2016 12:30–12:55, Dorodnitsyn Computing Centre, Department of Mechanics and Mathematics of Lomonosov Moscow State University., 119991, Moscow, Gubkina str., 8, Steklov Mathematical Institute, 9 floor, Conference hall

On the Bombieri-Pila method over function fields

A. A. Sedunova

Universite Paris-Sud 11, Faculte des Sciences d'Orsay, Orsay

Abstract: In 1989, E. Bombieri and J. Pila proved that if $\Gamma$ is a subset of an irreducible algebraic curve of degree $d$ inside a square of side $N$, then the number of lattice points on $\Gamma$ is bounded by $c(d,\varepsilon)N^{\frac{1}{d}+\varepsilon}$ for any $\varepsilon>0$, where the constant $c(d,\varepsilon)$ does not depend on $\Gamma$. We will establish a function field $\mathbb{F}_{q}$ analogue of this result.