DISCREPANCIES OF PRODUCTS OF ZETA-REGULARIZED PRODUCTS

作者：Castillo Garate Victor^*; Friedman Eduardo

来源：Mathematical Research Letters, 2012, 19(1): 199-212.

• Regularized products
• Dirichlet series

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 %26lt;br%26gt;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)). %26lt;br%26gt;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, %26lt;br%26gt;(Sigma(n)(j=1) deg P-j) F-n(P-1, ... ,P-n) = Sigma(1%26lt;i%26lt; j%26lt;n) (deg P-i + deg P-j) F-2(P-i, P-j). %26lt;br%26gt;Thus, there are no higher interactions behind the non-commutativity.

• 出版日期2012