Abstract: The Mahler measure of a complex polynomial is the geometric mean of that polynomial over the unit circle and acts as a height function. By a result of Kronecker, for nonconstant integer polynomials, the Mahler measure is equal to 1 if and only if all roots of the polynomial are 0 or roots of unity. In 1933, Lehmer asked if the Mahler measure for all other nonconstant integer polynomials had a lower bound greater than 1. This question has been studied extensively and remains an open problem in mathematics. We explore an analogue of this question using a generalization of the Mahler measure to lemniscates.
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