The even parity Goldfeld conjecture: congruent number elliptic curves

Ashay Burungale; Ye Tian

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The even parity Goldfeld conjecture: congruent number elliptic curves

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arxiv 2104.06732 v2 pith:TBU5FXJO submitted 2021-04-14 math.NT

Ashay Burungale , Ye Tian This is my paper

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keywords ellipticcongruentconjecturecurvesgoldfeldnumberanalyticarticle

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In 1979 Goldfeld conjectured: 50\% of the quadratic twists of an elliptic curve defined over the rationals have analytic rank zero. In this expository article we present a few recent developments towards the conjecture, especially its first instance - the congruent number elliptic curves.

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