Congruent numbers, elliptic curves, and the passage from the local to the global: an update

Abstract

This update to my article on Congruent numbers, elliptic curves, and the passage from the local to the global, which appeared in Resonance, December 2009, pp. 1183--1205 (https://www.ias.ac.in/describe/article/reso/014/12/1183-1205) and was posted here as arXiv:0704.3783, covers a few recent advances in the arithmetic of elliptic curves with special reference to the congruent number problem.