Arithmetic properties of automorphic forms and Drinfeld modules

自守形式和 Drinfeld 模的算术性质

• 批准号: 288296-2009
• 负责人: Kuo, Wentang
• 金额: $ 1.02万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=525770
• 关键词: Arithmetic; properties; automorphic; forms; Drinfeld

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.

我的研究领域是数论。一个数论对象可以与一个复函数相关联，这是数学中的一个常见现象，其中重要的算术数据被编码。例如，整数集可以与黎曼ζ函数相关联。特别是，整数中素数的分布可以与黎曼ζ函数的非平凡零点联系起来。我在数论方面的工作就是研究这些函数。我研究的一个领域是对一类复杂函数的非消失结果的研究。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。著名的费马定理是在1995年通过对这个问题的扩展研究得到证明的。Birch和Swinnerton-Dyer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函数之间的深刻联系。我关于这些函数的结果可以帮助我们更好地理解Birch和Swinnerton-Dyer的猜想。