On the Bombieri–Pila method over function fields
Volume 181 / 2017
Acta Arithmetica 181 (2017), 321-331
MSC: Primary 11P21; Secondary 14H05.
DOI: 10.4064/aa8613-8-2017
Published online: 4 December 2017
Abstract
E. Bombieri and J. Pila introduced a method for bounding the number of integral lattice points that belong to a given arc under several assumptions. We generalize the Bombieri–Pila method to the case of function fields of genus 0 in one variable. We then apply the result to counting the number of elliptic curves contained in an isomorphism class and with coefficients in a box.
