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On the Bombieri–Pila method over function fields

Volume 181 / 2017

Alisa Sedunova Acta Arithmetica 181 (2017), 321-331 MSC: Primary 11P21; Secondary 14H05. DOI: 10.4064/aa8613-8-2017 Published online: 4 December 2017


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.


  • Alisa SedunovaMathematisches Institut
    Universität Göttingen
    Bunsenstraße 3-5
    D-37073 Göttingen, Germany
    Max Planck Institute for Mathematics
    Vivatsgasse 7
    D-53111 Bonn, Germany

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