∀ {R : Type u_1} [inst : NormedCommRing R] [CompleteSpace R] {f : ArithmeticFunction R},
  f.IsMultiplicative → (Summable fun x => ‖f x‖) → ∏' (p : Nat.Primes), ∑' (e : ℕ), f (↑p ^ e) = ∑' (n : ℕ), f n