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    • Disparity in Selmer Ranks of Quadratic Twists of Elliptic Curves 

      Klagsbrun, Zev; Mazur, Barry Charles; Rubin, Karl (Princeton University, Department of Mathematics, 2013)
      We study the parity of 2-Selmer ranks in the family of quadratic twists of an arbitrary elliptic curve E over an arbitrary number field K. We prove that the fraction of twists (of a given elliptic curve over a fixed number ...