Almost all elliptic curves are Serre curves

Almost all elliptic curves are Serre curves

Using a multidimensional large sieve inequality, we obtain a bound for the mean square error in the Chebotarov theorem for division fields of elliptic curves that is as strong as what is implied by the Generalized Riemann Hypothesis. As an application we prove a theorem to the effect that, according...

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Bibliographic Details
Main Author: Jones, Nathan Conrad
Format: Dissertation
Language:English
Published: ProQuest Dissertations & Theses 01-01-2005
Subjects:
Mathematics
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Summary:Using a multidimensional large sieve inequality, we obtain a bound for the mean square error in the Chebotarov theorem for division fields of elliptic curves that is as strong as what is implied by the Generalized Riemann Hypothesis. As an application we prove a theorem to the effect that, according to height, almost all elliptic curves are Serre curves, where a Serre curve is an elliptic curve whose torsion subgroup, roughly speaking, has as much Galois symmetry as possible.
ISBN:9780542222016
0542222019