Breadcrumb
Polylogarithms and their functional equations
Wed 06 February 2013, 11:00
Matt Palmer
Bristol
Organiser: Tim Browning
ABSTRACT
Classical polylogarithms are a family of special functions defined by a
Taylor series which generalises that of the logarithm. These functions
have a variety of applications across mathematics, from simplifying
Feynman integrals to calculating volumes of hyperbolic 3-manifolds and
special values of Dedekind zeta functions; however, in this talk, I will
focus mainly on their functional equations.
I will first discuss the functional equations of classical polylogarithms,
and then how the polylogarithms can be adapted to give "cleaner"
functional equations, with no lower terms. Next, I will discuss how we can
define analogues of these polylogarithms in different spaces, and how the
functional equations for these polylogarithms can be obtained from the
original ones.
Finally, I will discuss finite polylogarithms - the analogue in Z/pZ - and
present two new functional equations for them.