Modifications to Klagsbrun-Mazur-Rubin yield bounds on Selmer rank distributions for Galois modules in p-cyclic extensions ordered by ramified primes, with applications to elliptic curve rank gains and point counts on superelliptic and hyperelliptic curves.
A Markov model for Selmer ranks in families of twists
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Distribution of Selmer ranks in prime cyclic extensions
Modifications to Klagsbrun-Mazur-Rubin yield bounds on Selmer rank distributions for Galois modules in p-cyclic extensions ordered by ramified primes, with applications to elliptic curve rank gains and point counts on superelliptic and hyperelliptic curves.