An Unexpected Connection between Elementary Sums of Quadratic
Functions and Modular Forms
By David Lowry
April 22, 2013
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.