On a basic mean value Theorem with explicit exponents

Abstract

In this paper we follow a paper from A. Sedunova (2017) regarding R. C. Vaughan's basic mean value Theorem (Acta Arith. 1980) to improve and complete a more general demonstration for a suitable class of arithmetic functions as started by A. C. Cojocaru and M. R. Murty (London Math. Soc. Stud. Texts 2006). As an application we derive a basic mean value Theorem for the von Mangoldt generalized functions.