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A Note on Lawton's Theorem

  Published:2016-11-29
 Printed: Sep 2017
  • Edward Dobrowolski,
    Mathematics Department, University of Northern British Columbia, Prince George, BC
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Abstract

We prove Lawton's conjecture about the upper bound on the measure of the set on the unit circle on which a complex polynomial with a bounded number of coefficients takes small values. Namely, we prove that Lawton's bound holds for polynomials that are not necessarily monic. We also provide an analogous bound for polynomials in several variables. Finally, we investigate the dependence of the bound on the multiplicity of zeros for polynomials in one variable.
Keywords: polynomial, Mahler measure polynomial, Mahler measure
MSC Classifications: 11R09, 11R06 show english descriptions Polynomials (irreducibility, etc.)
PV-numbers and generalizations; other special algebraic numbers; Mahler measure
11R09 - Polynomials (irreducibility, etc.)
11R06 - PV-numbers and generalizations; other special algebraic numbers; Mahler measure
 

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