In 1975 P.D.T.A. Elliott proved an interesting theorem on the existence of mean value for multiplicative functions. Elliott's paper is fairly complicated and the proofs require complex analysis, the dual of Turàn- Kubilius inequality and Halasz's method. In this paper we give an elementary proof of the first half of Elliott's theorem which avoids any use of complex analysis or Turàn-Kubilius type inequality and, instead, is based on computing the Ramanujan coefficients of the multiplicative function involved.
On Elliott's theorem on multiplicative functions
CODECA', Paolo;
1992
Abstract
In 1975 P.D.T.A. Elliott proved an interesting theorem on the existence of mean value for multiplicative functions. Elliott's paper is fairly complicated and the proofs require complex analysis, the dual of Turàn- Kubilius inequality and Halasz's method. In this paper we give an elementary proof of the first half of Elliott's theorem which avoids any use of complex analysis or Turàn-Kubilius type inequality and, instead, is based on computing the Ramanujan coefficients of the multiplicative function involved.File in questo prodotto:
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