OSU Mathematics Seminars and Colloquia
Calendar
Thu, Sep 22, 2022
Number Theory Seminar
3:30 PM
MSCS 514
Lower bounds for Mahler-type measures of polynomials
Igor Pritsker, OSU
[Abstract] [PDF]
Abstract: We consider various generalizations of the classical Mahler measure, and prove sharp lower bounds for them. For example, we show that for any monic polynomial $P \in {\mathbb C}[z]$ satisfying $|P(0)|=1$ the quantity $$M_0(P) = \exp\left(\frac{1}{2\pi}\int_0^{2\pi} \log^+|P(e^{i\theta})|\,d\theta\right)$$ is greater than or equal to $M(1+z_1+z_2)=1.381356\dots$. This inequality is best possible, and equality is attained for all $P(z)=z^n+c$ with $n \in {\mathbb N}$ and $|c|=1$. (Joint work with Arturas Dubickas.)
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