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Creators/Authors contains: "Rains, Eric"

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  1. ; ; (, Mathematische Annalen)
    Abstract Fix a positive integernand a finite field$${\mathbb {F}}_q$$ F q . We study the joint distribution of the rank$${{\,\mathrm{rk}\,}}(E)$$ rk ( E ) , then-Selmer group$$\text {Sel}_n(E)$$ Sel n ( E ) , and then-torsion in the Tate–Shafarevich group Equation missing<#comment/>asEvaries over elliptic curves of fixed height$$d \ge 2$$ d ≥ 2 over$${\mathbb {F}}_q(t)$$ F q ( t ) . We compute this joint distribution in the largeqlimit. We also show that the “largeq, then large height” limit of this distribution agrees with the one predicted by Bhargava–Kane–Lenstra–Poonen–Rains. 
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  2. ; ; ; ; (, Algebra & Number Theory)
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  3. ; ; (, Selecta Mathematica)
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