REU in Number Theory: Investigating Elliptic Curves, Modular Forms and Q-Series

数论中的 REU：研究椭圆曲线、模形式和 Q 级数

• 批准号: 0243604
• 负责人: Ken Ono
• 金额: $ 7.2万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-03-15 至 2004-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0243604&HistoricalAwards=false
• 关键词: REU; Number; Theory; Investigating; Elliptic

Eight undergraduate students with a solid background in mathematics will be selected to participate in a seven week Research Experience for Undergraduates to be held at the University of Wisconsin in Madison in the summer of 2003. The students will be exposed to specific questions in Number Theory involving elliptic curves, modular forms, orthogonal polynomials, and L-functions. The selected students will be offered up to $400 in travel support, free lodging, and a stipend of $3200.The students will be divided into two teams. One team will study orthogonal polynomials and their connection to supersingular elliptic curves, while the other will study generating functions for values of L-functions that are obtained by specializing the Fourier expansion of modular forms and various combinatorial q-series.

8名具有扎实数学背景的本科生将被选中参加2003年夏天在麦迪逊威斯康星大学举行的为期七周的本科生研究体验活动。学生将接触到数论中涉及椭圆曲线、模形式、正交多项式和L函数的具体问题。入选的学生将获提供高达400元的交通费、免费住宿和3200元津贴。学生将被分成两个小组。一个团队将研究正交多项式及其与超奇异椭圆曲线的联系，另一个团队将研究L函数的值的母函数，这些函数是通过专门研究模形式和各种组合Q-级数的傅里叶展开而获得的。