Distribution of zeros of entire functions of exponential growth

Abstract

For systems of equations with an infinite number of roots one can sometimes establish results of the type of the Kushnirenko–Bernstein–Khovanskii theorem by replacing the calculation of the number of the roots by the calculation of the asymptotic density of these roots. We consider systems of entire functions with exponential growth in $C^n$ and calculate the asymptotic behaviour of the averaged distribution of their zeros in terms of the geometry of convex bodies in a complex vector space.