Event Detail

Event Type: 
Number Theory Seminar
Date/Time: 
Tuesday, May 17, 2022 - 10:00 to 10:50
Location: 
Zoom only, contact Clayton Petsche for details

Speaker Info

Institution: 
Universit├Ąt Duisburg-Essen
Abstract: 

In order to measure the size of an algebraic number $\alpha$, Lehmer and Mahler (independently) introduced a quantity $M(\alpha)$ which is nowadays known as the Mahler measure of $\alpha$. One property of $M(\alpha)$ is that it is again an algebraic number. Hence, taking the Mahler measure defines a dynamical system on the set of algebraic numbers. We will study the possible size of the (forward) orbit of elements in this dynamical system. In particular, we will discuss the problem which number fields contain algebraic numbers with an infinite orbit. We can completely solve this problem for abelian number fields and number fields with a symmetric Galois group over the rationals. This is joint work with P. Fili and M. Zhang.