Asymptotic results for average sizes of isogeny Selmer groups of hyperelliptic Jacobians are obtained by combining Bhargava geometry-of-numbers with new Vinberg-theory parametrizations for Dynkin types B and C, plus lower bounds via Greenberg-Wiles.
[Lan75] Serge Lang.SL 2(R)
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Arithmetic statistics of isogeny Selmer groups associated to hyperelliptic curves
Asymptotic results for average sizes of isogeny Selmer groups of hyperelliptic Jacobians are obtained by combining Bhargava geometry-of-numbers with new Vinberg-theory parametrizations for Dynkin types B and C, plus lower bounds via Greenberg-Wiles.