Outline of a Theory of Arithmetical Functions in their Algebraic Aspects

Your recent note in the Journal, (Vol. 17, No. 5, October 1927, pp. 69—73), on the Inversion of Multiplicative Arithmetical Functions, was of particular interest to me, as I have used the same method for several years in precisely your form of it, also in an extended sense. Thinking that you might like to hear of some of this work, especially in view of your remarks concerning your main result: "The theorem (2) is a fundamental one in the whole theory of Arithmetic Functions. It is rather surprising that it does not seem to have been utilised before (at any rate so far as one can see from Dickson's History).