Rank statistics for a family of elliptic curves over a function field | Macquarie University ResearchOnline

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Title: Rank statistics for a family of elliptic curves over a function field
Related: Pure and applied mathematics quarterly, Vol. 6, No. 1, (2010), p.21-40
Related: http://www.intlpress.com/JPAMQ/2010-index/PAMQ-vol-6-1.php#PAMQ-6-1
Publisher: International Press
Date: 2010
FoR/RFCD Code(s): 010200 Applied Mathematics 010100 Pure Mathematics
Author/Creator: Pomerance, Carl
Author/Creator: Shparlinski, Igor E
Description: 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.
Description: 20 page(s)
Subject Keyword: 010200 Applied Mathematics
Subject Keyword: 010100 Pure Mathematics
Subject Keyword: rank of elliptic curve
Subject Keyword: function field
Subject Keyword: multiplicative order
Resource Type: journal article
Organisation: Macquarie University. Dept. of Computing

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