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

Published online by Cambridge University Press:  09 April 2009

P. D. T. A. Elliott
P. D. T. A. Elliott
Affiliation:
Univesity of Colorado, Boulder, Colorado, U.S.A.
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Abstract

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On analogy with functions if Lebesuge class Lα on the real line the author considers those multiplicative arthmetic functions which are bounded in mean α>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 τ-function.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 2 , March 1980 , pp. 177 - 205
Copyright
Copyright © Australian Mathematical Society 1980

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