Elliptic Curves and L-functions

这个研究项目是在数论领域，这是数学的一部分，涉及整数的性质和整数系数方程的解。这样的方程称为丢番图方程。椭圆曲线是丢番图方程理论的基本研究对象之一。椭圆曲线的研究可以用代数、分析和几何的方法进行。在过去的十年中，我研究了几个问题，在这方面从分析的角度来看，并采用L-函数，这是基本的工具，在解析数论。

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.