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Average size of 2-Selmer groups of elliptic curves, II

2005
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Acta Arithmetica
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A natural question to ask is about the average order of Sel 2 (E(a, b)) with one variable, say b, varying over a certain interval. If one could show that the average order of the 2-Selmer groups of E(a, b) with b running over every interval of size between |a| 1−ε and |a| 1+ε was uniformly bounded as |a| → ∞, then (1.2) would be obviously true. Unfortunately, the average order of Sel 2 (E(a, b)) in this sense depends on a quite complicatedly, and it is not possible to get a uniform estimate for

doi:10.4064/aa117-1-1
fatcat:75tjnxvrcna7bhsjtsb3z6t6me