A Note on Lawton's Theorem

  title={A Note on Lawton's Theorem},
  author={Edward G. Dobrowolski},
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 coeõcients takes small values. Namely, we prove that Lawton’s bound holds for polynomials that are not necessarilymonic. We also provide an analogous bound for polynomials in several variables. Finally, we investigate the dependence of the bound on themultiplicity of zeros for polynomials in one variable. 

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