In this paper we study a problem related to Ramanujan's expansions of multiplicative functions also considered by H.Delange in 1984.We prove the existence of the mean value of certain arithmetical convolutions and also obtain its integral representation.This gives the possibility of computing immediately the Ramanujan coefficients of the arithmetical functions involved. In this way we obtain a short proof of Delange's theorem.We also obtain a new summability result.
A note on Ramanujan coefficients of arithmetical functions
CODECA', Paolo
1991
Abstract
In this paper we study a problem related to Ramanujan's expansions of multiplicative functions also considered by H.Delange in 1984.We prove the existence of the mean value of certain arithmetical convolutions and also obtain its integral representation.This gives the possibility of computing immediately the Ramanujan coefficients of the arithmetical functions involved. In this way we obtain a short proof of Delange's theorem.We also obtain a new summability result.File in questo prodotto:
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