Elliptic Curves and L-functions

这个研究项目属于数论领域，数论是数学中处理整数性质和整数系数方程解的部分。这样的方程叫做丢番图方程。椭圆曲线是丢番图方程理论的基本研究对象之一。椭圆曲线的研究适用于代数、分析和几何的方法。在过去的十年里，我从分析的角度研究了这个领域的几个问题，并使用了解析数论中的基本工具l -函数。

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.