OSU Mathematics Seminars and Colloquia
Calendar
Tue, Apr 26, 2022
Number Theory Seminar
10:30 AM
MSCS 509
Lehmer's Problem for Polynomials Having Small Mahler Measure on Bernoulli's Lemniscate
Ryan Looney, Oklahoma State University
Note that this talk is on a Tuesday, not Thursday.
[Abstract] [PDF]
Abstract: The Mahler measure of a complex polynomial is the geometric mean of that polynomial over the unit circle. By a result of Kronecker, for nonconstant integer polynomials, the Mahler measure is equal to 1 if and only if all roots of the polynomial are 0 or roots of unity. In 1933, Lehmer asked if the Mahler measure for all other nonconstant integer polynomials had a lower bound greater than 1. In fact, Lehmer noted that the smallest such measure he had found belonged to a polynomial having degree 10, and to this day no polynomial has been found which lowers this bound. We explore a generalization of the Mahler measure and Lehmer's problem over the classical Bernoulli's lemniscate and its variations.
Automatically add seminars to your own calendar (e.g., Google Calendar) via an ical link.

List of links (urls) directly to a seminar series.

Return to Math Department Login Page

To add/edit talks, please log in on the department web page, then return to Announce.
Alternatively if you know the Announce username/password, click the link below:

Announce Seminar Calendar Login