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.
|Number of pages||20|
|Journal||Pure and Applied Mathematics Quarterly|
|Publication status||Published - Jan 2010|