Number theory in function fields

函数域中的数论

• 批准号: 261908-2011
• 负责人: Liu, YuRu
• 金额: $ 1.89万
• 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: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508805
• 关键词: Number; theory; function; fields

Classically, number theory is the study of arithmetic properties of integers. My research focuses on the interplay between this theory, and the theory of a related object, the set of polynomials over a finite field. The set of integers, and the aforementioned set of polynomials have ostensibly different structures. For example, given a non-zero integer, no multiple of it is zero. However, a fixed finite field always admits a prime number p for which any p-multiple of an element is zero, hence this property is carried over to polynomials on this field. Despite these apparent differences, it is a striking theme in arithmetic that there are remarkable similarities between these two sets.

经典的数论是研究整数的算术性质的。我的研究集中在这个理论和一个相关对象的理论之间的相互作用，有限域上的多项式集。整数集和前面提到的多项式集具有表面上不同的结构。例如，给定一个非零整数，它的任何倍数都不是零。然而，一个固定的有限域总是允许一个素数p对其元素的任意p倍数为零，因此这一性质被推广到这个域上的多项式。尽管有这些明显的差异，但在算术中，这两组之间有显著的相似之处，这是一个引人注目的主题。