Authors and affiliations
Kenneth R. Johnson
North Dakota State University
The theory of Dirichlet series having number theoretic functions of a single variable as coefficients has a rich history. In this paper we present a parallel theory for iterated Dirichlet series with number theoretic functions of two variables as coefficients and find the Dirichlet product inverse of Ramanujan’s sum. The results presented here are easily accessible to an Advanced Calculus or undergraduate Number Theory course.
- D. R. Anderson and T. M. Apostol, The Evaluation of Ramanujan’s Sum and Generalizations, Duke Journal, 20 (1953), 211-216.
- Tom M. Apostol, Introduction to Analytic Number Theory, New York-Heidelberg-Berlin: Springer-Verlag(1976).
- S. Ramanujan, On certain trigonometrical sums and their applications in the theory of numbers, Cambridge Philosophical Transactions, 22 (1918), 259-276.
Cite this paper
Johnson, K. R. (2003). Iterated Dirichlet series and the inverse of Ramanujan’s sum. Notes on Number Theory and Discrete Mathematics, 9(3), 65-72.