Event Detail

Event Type: 
Number Theory Seminar
Tuesday, October 10, 2017 - 16:00 to 17:00
STAG 112

Speaker Info

Mathematics Department, University of Texas

We will describe Lehmer’s problem about small values of Mahler’s measure (or small values of the Weil height). Then we will give a mostly expository account of several Diophantine questions that are related in a simple way to the Lehmer problem. In some cases the Diophantine question is known to be equivalent to the Lehmer problem. For example: does there exist a monic polynomial F(x) with coefficients in the set {−1,0,1}, and having a complex root outside the unit disk of multiplicity greater than or equal to N? Our ability to construct such a polynomial is currently limited by our understanding of Lehmer’s problem. At present it is known that such polynomials exist if N = 4, but the problem is open for N = 5.