80 citations · 218 across the 21 of their papers we have counts for
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math.NT2009★ 19 cited
Refined class number formulas and Kolyvagin systems
Barry Mazur, Karl Rubin
We use the theory of Kolyvagin systems to prove (most of) a refined class number formula conjectured by Darmon. We show that for every odd prime , each side of Darmon's conjectu…
math.NT2009★ 80 cited
Ranks of twists of elliptic curves and Hilbert's Tenth Problem
Barry Mazur, Karl Rubin
In this paper we investigate the 2-Selmer rank in families of quadratic twists of elliptic curves over arbitrary number fields. We give sufficient conditions on an elliptic curve s…