Arithmetic properties of automorphic forms and Drinfeld modules

我的研究领域是数论。 数论对象可以与复变函数相联系是数学中的一种常见现象，其中重要的算术数据被编码。例如，整数的集合可以与黎曼zeta函数相关联。特别地，素数在整数中的分布可以与黎曼zeta函数的非平凡零点相关联。我在数论方面的工作就是研究这些函数。我工作的一个领域是研究非零结果的某些家庭的这种复杂的功能。我研究的另一个领域是椭圆曲线。椭圆曲线的研究在现代数论中占有重要地位。著名的费马定理在1995年通过对这个问题的深入研究得到了证明。Birch和Swinnerton-Dyer提出的一个猜想预言了椭圆曲线的算术数据与椭圆曲线上的复变函数之间的深层联系。这些结果有助于我们更好地理解Birch和Swinnerton-Dyer猜想。

My research area is number theory. It is a common phenomenon in mathematics that a number theoretical object can be associated with a complex function, in which important arithmetic data are encoded. For instance, the set of integers can be associated with the Riemann zeta function. In particular, the distribution of primes in integers can be associated with the non-trivial zeros of the Riemann zeta function. My work on number theory is to study these functions. One area I work in is the study of non-vanishing results on a certain family of such complex functions. Another area I work in is elliptic curves. The study of elliptic curves is important in modern number theory. The famous Fermat theorem was proved in 1995 by extended studies on this subject. A conjecture made by Birch and Swinnerton-Dyer predicts the deep connection between the arithmetic data of elliptic curves and the complex functions attached to elliptic curves. My results on these functions can help us better understand the conjecture of Birch and Swinnerton-Dyer.