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On elliptic curves of bounded degree:a polarized Abelian surface
Guerra, Lucio
2016
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e-ISSN
2464-8728
Abstract
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.
Series
Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics
48 (2016)
Publisher
EUT Edizioni Università di Trieste
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