Bulletin of the Australian Mathematical Society

Research Article

On measures of polynomials in several variables

C.J. Smytha1

a1 Department of Mathematics, James Cook University, Townsville, Queensland 4811, Australia.


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.

(Received August 06 1980)