An Unexpected Connection between Elementary Sums of Quadratic Functions and Modular Forms

By David Lowry

April 22, 2013

Abstract

In this talk, we will start by considering an elementary-seeming sum over quadratic functions and examine some surprising properties about it. We generalize and find a pattern. But then the pattern will be ruined, and the cause is somehow deeply connected to modular forms. This talk is very elementary and totally approachable, although there will be brief forays into aspects of number theory throughout.