most citedThe Parity of Analytic Ranks among Quadratic Twists of Elliptic Curves over Number Fields

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math.NT2014★ 3 cited

The Parity of Analytic Ranks among Quadratic Twists of Elliptic Curves over Number Fields

Nava Balsam

The parity of the analytic rank of an elliptic curve is given by the root number in the functional equation L(E,s). Fixing an elliptic curve over any number field and considering t…