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

将选出8名具有扎实数学背景的本科生参加2003年夏天在威斯康星大学麦迪逊分校举行的为期7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。被选中的学生将获得高达400美元的旅行支持，免费住宿和3200美元的津贴。学生们将被分成两队。一个小组将研究正交多项式及其与超奇异椭圆曲线的联系，而另一个小组将研究l函数值的生成函数，这些函数是通过专门研究模形式的傅立叶展开和各种组合q级数获得的。

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.