Abstract: For the classical Mahler measure, there exists a sharp lower bound for the measure of totally real integer polynomials which was proven by a result of Schinzel. For a generalization of the Mahler measure on lemniscates, we prove an analogous lower bound for the measure of totally real integer polynomials. Our proof generalizes a well-known known proof by Höhn and Skoruppa of the classical Schinzel result, which we show in detail. We describe how to determine whether this analogous lower bound is sharp, as in the classical case, or if it can be improved. Using this description, we detail our computational results in the search for lemniscates where the Mahler measure attains this lower bound. This is a joint work with Igor Pritsker.
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