Abstract
We show that the average and typical ranks in a certain parametric family of elliptic curves described by D. Ulmer tend to infinity as the parameter d → ∞. This is perhaps unexpected since by a result of A. Brumer, the average rank for all elliptic curves over a function field of positive characteristic is asymptotically bounded above by 2.3.
Original language | English |
---|---|
Pages (from-to) | 21-40 |
Number of pages | 20 |
Journal | Pure and Applied Mathematics Quarterly |
Volume | 6 |
Issue number | 1 |
Publication status | Published - Jan 2010 |