The even parity Goldfeld conjecture: congruent number elliptic curves
arXiv:2104.06732
Abstract
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.
20 pages