Mathematical Sciences: Explicit Reciprocity Laws in Algebraic Number Fields and Algebraic Function Fields

这项资助是为摩拉维亚学院的4名学生在夏季的本科生研究经历网站提供的。该项目将为本科生提供一个数学学习和研究的机会，为他们提供研究生院式的经验。首席研究员将在整个八周的项目中监督一个研讨会。起初，研讨会将介绍必要的背景材料，逐渐地，学生们将积极参与到研讨会中，就课外读物发表演讲，并做自己的研究。学生研究项目的选择是为了方便本科生使用。该项目的主要焦点是在代数数论的显互易律的领域。每个学生的研究课题都将与这个中心问题相关，但重点是一个特定的方面，可以从以下内容中选择一个：有限域、有限域上的多项式和一元代数函数、互易映射和某些多项式的显式分解。

This grant is for an Research Experiences For Undergraduates site for 4 students at Moravian College during the summer. The project will offer the undergraduates an opportunity for mathematical study and research by providing them a graduate school type experience. The Principal Investigator will supervise a seminar throughout the entire eight weeks of the program. Initially the seminar will introduce necessary background material, and gradually the students will become actively involved in the seminar, giving talks on outside readings as well as doing their own research. The student research projects have been chosen so that they are accessible to undergraduates. The main focus of the project is in the area of explicit reciprocity laws in algebraic number theory. Each student's research topic will relate to this central problem but focus on a particular aspect which may be chosen from one of the following: finite fields, polynomials and algebraic functions in one variable over finite fields, reciprocity maps, and explicit factorization of certain polynomials.