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Title: On elliptic curves of bounded degree:a polarized Abelian surface
Authors: Guerra, Lucio
Keywords: Elliptic curveAbelian surfacepolarizationlattice points
Issue Date: 2016
Publisher: EUT Edizioni Università di Trieste
Series/Report no.: Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics
48 (2016)
For a polarized compleax Abelian surface A we study the function NA(t) counting the number of elliptic curves in A with degree bounded by t. We describe elliptic curves as solutions of an explicit Diophantine equation, and we show that computing the number of solutions is reduced to the classical problem in Number Theory of counting lattice points lying on an explicit bounded subset of Euclidean space. We obtain in this way some asymptotic estimate for the counting function.
Type: Article
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/13169
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.48 (2016)

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