关于数论中从局部到整体的过渡

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

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.

Local and global methods in arithmetic（俄语）

Local and global methods in arithmetic (in Russian)

设$p$为素数。我们讨论使用$p$ -进数的同余模$p^n$的解决方案的方法，这些方法是类似的计算与实数（本地方法）。本地和全球的方法之间的关系的例子给出生产一个通道，从同余式解决方案的整数（全球性的方法）。本文介绍了用计算机研究$p$ -进数和代数曲线的方法。