artículo
DISCREPANCIES OF PRODUCTS OF ZETA-REGULARIZED PRODUCTS
Fecha
2012Registro en:
1945-001X
1073-2780
WOS:000305635800016
Autor
Castillo Garate, Victor
Friedman, Eduardo
Institución
Resumen
Zeta-regularized products (Pi) over cap (m) a(m) are known not to commute with finite products, so one studies the discrepancy F-n given by exp(F-n) := (Pi) over cap (m) (Pi(n)(j=1) a(m,j))/Pi(n)(j=1) ((Pi) over cap (m)a(m,j)). 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, (Sigma(n)(j=1) deg P-j) F-n(P-1, ... ,P-n) = Sigma(1<i< j<n) (deg P-i + deg P-j) F-2(P-i, P-j). Thus, there are no higher interactions behind the non-commutativity.