The multiplicative anomaly of three or more commuting elliptic operators

Victor Castillo-Garate, Eduardo Friedman, Marius Mantoiu
2015 Mathematical Research Letters  
ζ-regularized determinants are well-known to fail to be multiplicative, so that in general det ζ (AB) = det ζ (A) det ζ (B). Hence one is lead to study the n-fold multiplicative anomaly We show that if the A i are commuting pseudo-differential elliptic operators, then their joint multiplicative anomaly can be expressed in terms of the pairwise multiplicative anomalies. Namely where m j is the order of A j . The proof relies on Wodzicki's 1987 formula for the pairwise multiplicative anomaly M 2
more » ... cative anomaly M 2 (A, B) of two commuting elliptic operators.
doi:10.4310/mrl.2015.v22.n3.a2 fatcat:3ktmzyw7rre4dk5gl6fauzc64e