Abstract: For the classical Mahler measure $M(P)$, the minimal measure $M(P)>1$ for a totally real polynomial $P$ is well understood. By a result of Schinzel, the value of $M(P)$ increases exponentially with respect to the degree of totally real $P$. For a generalization of the Mahler measure over lemniscates, we investigate an analogous bound to the classical bound of Schinzel. We describe lemniscates, and their respective polynomials, for which this analogous bound is sharp, and also lemniscates for which this analogous bound can be improved. This is a joint work with Igor Pritsker.
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