Geodesic
On the Bombieri–Pila method over function fields
Alisa Sedunova1
1 Mathematisches Institut Universität Göttingen Bunsenstraße 3-5 D-37073 Göttingen, Germany and Max Planck Institute for Mathematics Vivatsgasse 7 D-53111 Bonn, Germany
Acta Arithmetica, Tome 181 (2017) no. 4, pp. 321-331

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/aa8613-8-2017
Keywords: bombieri pila introduced method bounding number integral lattice points belong given arc under several assumptions generalize bombieri pila method function fields genus variable apply result counting number elliptic curves contained isomorphism class coefficients box

Alisa Sedunova 1

1 Mathematisches Institut Universität Göttingen Bunsenstraße 3-5 D-37073 Göttingen, Germany and Max Planck Institute for Mathematics Vivatsgasse 7 D-53111 Bonn, Germany 
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Alisa Sedunova. On the Bombieri–Pila method over function fields. Acta Arithmetica, Tome 181 (2017) no. 4, pp. 321-331. doi: 10.4064/aa8613-8-2017

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