Event Type:

Number Theory Seminar

Date/Time:

Tuesday, October 10, 2017 - 16:00 to 17:00

Location:

STAG 112

Guest Speaker:

Jeff Vaaler

Institution:

Mathematics Department, University of Texas

Abstract:

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.