On measures of polynomials in several variables-Reference-Cited by-同舟云学术

On measures of polynomials in several variables

Published:1981-02 Issue:1 Volume:23 Page:49-63
ISSN:0004-9727
Container-title:Bulletin of the Australian Mathematical Society
language:en
Short-container-title:Bull. Austral. Math. Soc.

Author:

Smyth C.J.

Abstract

The measure of a polynomial is defined as the exponential of a certain intractable-looking integral. However, it is shown how the measures of certain polynomials can be evaluated explicitly: when all their irreducible factors are linear, and belong to one of two special classes. Asymptotic values for the measures of two sequences of polynomials in large numbers of variables are also found. The proof of this result uses a quantitative form of the central limit theorem.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference7 articles.

1. A Kronecker-type theorem for complex polynomials in several variables;Smyth;Canad. Math. Bull.

2. Kronecker's theorem and Lehmer's problem for polynomials in several variables;Boyd;J. Number Theory

3. Speculations concerning the range of Mahler's measure;Boyd;Canad. Math. Bull.

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