Discrepancies of products of zeta-regularized products

Abstract

Zeta-regularized products Πmam are known not to commute with finite products, so one studies the discrepancy Fn given by exp(Fn) := {equation presented}. For a rather general class of products, associated to polynomials Pj in several variables, we show that the discrepancy Fn(P1, . . . , Pn) of n products is a sum of pairwise contributions F2(Pi, P j). Namely, {equation presented}. Thus, there are no higher interactions behind the non-commutativity. © International Press 2012.