“…Then, let Z(z, χ) := a∈G χ(a)z ∂(a) , (1.2) where the summation is taken over all a ∈ G in an ascending order of ∂(a). As in [3], Z(z, χ) is called a zeta function on the formation (G, ∂, ∼). For an additive formation (G, ∂, ∼) satisfying Axiom B, Z(z, χ) is holomorphic and has no zeros in the open disk {|z| < q −1 } due to an analogue of the Euler product formula.…”