Rank statistics for a family of elliptic curves over a function field

Carl Pomerance*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)21-40
Number of pages20
JournalPure and Applied Mathematics Quarterly
Volume6
Issue number1
Publication statusPublished - Jan 2010

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