Discrepancies of products of zeta-regularized products

摘要

Zeta-regularized products Π _ma _m are known not to commute with finite products, so one studies the discrepancy F _n given by exp(F _n):= {equation presented}. For a rather general class of products, associated to polynomials P _j in several variables, we show that the discrepancy F _n(P _1, . . ., P _n) of n products is a sum of pairwise contributions F _2(P _i, P _j). Namely, {equation presented}. Thus, there are no higher interactions behind the non-commutativity.