Tenth Algorithmic Number Theory Symposium ANTSX

Conditionally bounding analytic ranks of elliptic curves
Jonathan Bober
Abstract: We describe a method for bounding the rank of an elliptic curve under the assumptions of the Birch and SwinnertonDyer conjecture and the generalized Riemann hypothesis. As an example, we compute, under these conjectures, exact upper bounds for curves which are known to have rank at least as large as 20, 21, 22, 23, and 24. For the known curve of rank at least 28, we get a bound of 30.
Files available: paper (PDF)
© 201112 Kiran S. Kedlaya (with thanks to Pierrick Gaudry and Emmanuel ThomÃ©)
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