同余数问题、整二次型和代数K理论相关问题的研究

本项目将致力于数论和 K 理论中下列相关问题的研究并取得新的成果：同余数问题、带复乘的椭圆曲线的 Lang-Trotter 猜想、整二次型表整数问题、椭圆曲线的 K-理论和 Mahler 测度之间的关系、动力系统的算术. 研究中使用并且发展我们已有的独创方法.

This project seeks to make significant progress in the study of the following related problems: the congruent number problem, the Lang-Trotter conjecture of CM elliptic curves, representations of some integral quadratic forms， the relationship between the Mahler measure and the K-theory of elliptic curves, the arithmetic of dynamical systems. We will develop useful techniques to strengthen our original methods.