| Rank statistics for a family of elliptic curves over a function field (2009) | |||||||||
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 $d \to\infty$. 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. | |||||||||
Details der Publikation | |||||||||
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