Published on *Max Planck Institute for Mathematics* (https://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Jeffrey Vaaler
Affiliation:

The University of Texas at Austin
Date:

Thu, 2019-04-04 11:15 - 12:15 We prove a new lower bound for the Mahler measure of a polynomial in one and

in several variables that depends on the complex coefficients and the number of

monomials, but not on the degree. In one variable the lower bound generalizes a

classical inequality of Mahler. In M variables the inequality depends on Z^M as an

ordered group, and in general the lower bound depends on the choice of ordering. In

one variable the proof is elementary. In M variables the proof exploits an idea used

in earlier work of D. Boyd. The talk should be accessible to a general mathematical

audience. This is joint work with S. Akhtari.

**Links:**

[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] https://www.mpim-bonn.mpg.de/node/3444

[3] https://www.mpim-bonn.mpg.de/node/246