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Tuesday, June 12, 2018 - 17:15 in X-E0-218

Mahler measures, the Lehmer Conjecture, and its consequences

A talk in the SYMBol series by
Neil Manibo

Abstract: Given a polynomial with integer coefficients, its Mahler measure is defined to be its geometric mean on the unit circle. This talk will center on the still open Lehmer's problem, which asks whether such a measure is bounded away from one outside the class of cyclotomic polynomials. In particular, the progression of partial results and proofs on subclasses will be laid out, as well as exhaustive searches for polynomials with small measures. We then mention some of its implications and connections to other gap results in number theory, ergodic theory, and geometric group theory.


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