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On an arithemtical inequality

Published online by Cambridge University Press:  18 May 2009

S. Srinivasan
S. Srinivasan
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India
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Here we extend an arithmetical inequality about multiplicative functions obtained by K. Alladi, P. Erdős and J. D. Vaaler, to include also the case of submultiplicative functions. Also an alternative proof of an extension of a result used for this purpose is given.

Let Uk, for integral k, denote the set {1,2,…, k}, and Vk denote the collection of all subsets of Uk. In the following, all unspecified sets like A,…, are assumed to be subsets of Uk. Let σ = {Si} and τ = {Tj} be two given collections of subsets of Uk. Set

and

Let ′ denote complementation in Uk (but for in the proof of (3) where it denotes complementation in C). For any collection p of subsets of Uk, let p′ denote the collection of the complements of members of p.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 1 , January 1994 , pp. 81 - 86
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

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