Event Detail

Event Type: 
REU Colloquium
Monday, July 17, 2017 - 10:00 to 11:00
STAG 112

The Mahler measure of a polynomial is the product of the leading coefficient, and the modulus of all roots which fall outside the unit circle. Lehmer conjectured that the smallest Mahler measure of a polynomial with integer coefficients, strictly greater than 1, is approximately 1.176. Lehmer found a tenth degree polynomial with Mahler measure 1.176 in 1933, by hand, and no amount of computing power in the last eighty years has been able to improve on this bound. In this talk, we will look at the history of the topic, as well as what partial results have been found.