Holly Krieger : Zsigmondy Sets in Arithmetic Dynamics

Posted by Holly Krieger , part of the Graduate Number Theory Seminar.

At

April 20, 2011, 3 p.m.

In

SEO 427

Abstract

I will discuss a result of Silverman and Ingram on the finitude of the Zsigmondy set associated to the forward orbit of a wandering point of a rational map of degree at least 2, defined over a number field, which has 0 periodic. The Zsigmondy set of a sequence (a_n) is the set of indices so that a_n does not have a primitive prime divisor. I will prove the easy generalization to the case of 0 preperiodic, and discuss my progress on further generalizations.