Finite products of regularized products

Abstract

The product ((Pi) over cap (m) a(m)) . ((Pi) over cap (m)b(m)) of two regularized products is not in general equal to the regularized product (Pi) over cap (m) (a(m) . b(m)) We consider the discrepancy F, defined by exp(F):= (Pi) over cap (m)(a(m) . b(m))/((Pi) over cap (m)a(m)).((Pi) over cap (m)b(m)).

When the terms a(m) and b(m) depend on parameters, we show in certain cases that F is a polynomial in these parameters.