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

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

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.