Mean Value theorems for multiplicative functions bounded in mean α-power, α 1

摘要

On analogy with functions if Lebesuge class L?± on the real line the author considers those multiplicative arthmetic functions which are bounded in mean ?±>1. Necessary and sufficient conditions are obtained in order that they should have a mean-value, zero or non-zero. An application is made to Ramanujan's ??-function.