AN ARITHMETIC FORMULA OF LIOUVILLE TYPE AND AN EXTENSION OF AN IDENTITY OF RAMANUJAN
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.
arithmetic formula of Liouville type, Ramanujan?s identity.
