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 |