Abstract
AbstractWe define a notion of measure for polynomials in several variables, basing our construction on the geometry of the zero-set of the polynomial. For polynomials in one variable, this measure reduces to the usual one. We begin the development of the theory of this measure along lines parallel to the theory of Mahler’s measure, indicating the differences and similarities between the two.Let P be a polynomial in one variable with complex coefficients, P(z) = a0Π(z - αj). The measure of P, denoted M(P), is defined by1As is well-known, an application of Jensen’s formula yields2
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