AN ARITHMETIC FORMULA OF LIOUVILLE TYPE AND AN EXTENSION OF AN IDENTITY OF RAMANUJAN

Erin McAfee (Canada) and Kenneth S. Williams (Canada)

Abstract

Let Let be an odd function. An arithmetic identity of Liouville type is proved in an elementary manner for the sum see Theorem 1.2. As an application of this formula, an identity for the cube of the Lambert series is obtained analogous to that of Ramanujan for the square of this series, see Theorem 1.1.

Keywords and phrases: arithmetic formula of Liouville type, Ramanujan’s identity.