A problem of Boyd concerning geometric means of polynomials |
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Authors: | Wayne M Lawton |
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Institution: | Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, California 91103 USA |
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Abstract: | In this paper we derive an equality which characterizes the distribution of the modulus of a polynomial on the unit circle. This inequality is used to prove a conjecture of Boyd concerning the geometric mean of the modulus of a polynomial of several variables averaged over the torus. References are cited which discuss the relationship of this conjecture to a classical question of Lehmer concerning the distribution of roots of polynomials. |
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