Rank statistics for a family of elliptic curves over a function field
نویسندگان
چکیده
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. 2000 Mathematics Subject Classification: 11N25, 11R37, 14H52 The first author was supported in part by NSF grant DMS-0401422. The second author was supported in part by ARC grant DP0556431. 1
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