Generating function zeros for hadron multiparticle distributions

A theorem is proved that delineates criteria for the radii of the annulus of the zeros in the complex plane of the generating function for factorial moments as it applies to high-energy charged-hadron multiproduction. It is shown how this theorem and the general features of the negative binomial distribution provide an explanation of the distribution of generating-function zeros along an open circular ring of approximately unit radius found in simulations and collider data. {copyright} {ital 1997} {ital The American Physical Society}