Counting elliptic curves of bounded Faltings height

• Autorzy: Ruthi Hortsch
• Języki publikacji: EN

Abstrakty

EN

We give an asymptotic formula for the number of elliptic curves over ℚ with bounded Faltings height. Silverman (1986) showed that the Faltings height for elliptic curves over number fields can be expressed in terms of modular functions and the minimal discriminant of the elliptic curve. We use this to recast the problem as one of counting lattice points in a particular region in ℝ².

Kategorie tematyczne

• 11G05: Elliptic curves over global fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 173
• Numer: 3
• Strony: 239-253

Daty

wydano

2016

Twórcy

autor

Ruthi Hortsch

• Department of Mathematics, 2-239A, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, U.S.A.

Identyfikatory

DOI

10.4064/aa8204-2-2016