∀ {f g : ArithmeticFunction ℂ} {s : ℂ},
  (LSeries.abscissaOfAbsConv fun n => f n) < ↑s.re →
    (LSeries.abscissaOfAbsConv fun n => g n) < ↑s.re →
      LSeries (fun n => (f * g) n) s = LSeries (fun n => f n) s * LSeries (fun n => g n) s