Elliptic Curves and L-functions

这个研究项目是在数论领域，数论是数学的一部分，处理整数的性质和具有整数系数的方程的解。这样的方程称为丢番图方程。椭圆曲线是丢番图方程论中的基本研究对象之一。椭圆曲线的研究可以用代数、分析和几何的方法。在过去的十年里，我从解析的角度，利用L函数这一解析数论的基本工具，研究了这方面的几个问题。

This research program is in the field of number theory, which is the part of mathematics that deals with properties of integers and solutions of equations with integer coefficients. Such equations are called Diophantine equations. Elliptic curves are one of the fundamental objects of study in the theory of Diophantine equations. The study of elliptic curves is amenable to methods from algebra, analysis, and geometry. Over the past decade, I have studied several problems in this area from an analytic point of view and by employing L-functions which are fundamental tools in analytic number theory.