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Lower bounds for Mahler measure that depend on the number of monomials

Posted in
Speaker: 
Jeffrey Vaaler
Zugehörigkeit: 
The University of Texas at Austin
Datum: 
Don, 2019-04-04 11:15 - 12:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

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.

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