On the relation between the generalized Pauli-Villars and the covariant regularization

Some aspects of the comparison that has been established recently by Fujikawa between the generalized Pauli-Villars regularization and the covariant regularization of composite current operators are investigated, in particular, the fundamental question of the choice of regulator, satisfying appropriate conditions. The notion of zeta function of the operators is basic in the discussion. While developing the method, some new formulas that are very useful in physical applications of the theory are given.