Speaker: Guoce Xin (Brandeis)
Title: A new algorithm on PFD and its application to generalized Dedekind sums
Abstract: Recently, I developed a new algorithm on PFD - partial fraction decomposition of rational functions. This new algorithm is not only fast but also has theoretical applications.
Given a rational function R(x), the generalized Dedekind sum is the sum of R(a) over all nth roots of unity a (often with a = 1 excluded). Such problems arise in several areas of mathematics, such as number theory and topology.