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An Optimization Problem Related to the Zeta-function

Published online by Cambridge University Press:  20 November 2018

Silviu Guiasu
Silviu Guiasu*
Affiliation:
Department of Mathematics, York University 4700 Keele Street, North York, Canada M3J 1P3
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Abstract

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S. Golomb noticed that Riemann's zeta function ζ induces a probability distribution on the positive integers, for any s > 1, and studied some of its properties connected to divisibility. The object of this paper is to show that the probability distribution mentioned above is the unique solution of an entropy-maximization problem.

Keywords

Riemann's zeta functionShannon's entropythe maximum entropy probability distribution.Primary10K99Secondary62E1594A17

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986, pp. 70 - 73
Copyright
Copyright © Canadian Mathematical Society 1986

References

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3. Guiasu, S.,Information Theory with Applications, McGraw-Hill, New York—Düsseldorf— London, 1977.Google Scholar
4. Guy, R. K., Unsolved Problems in Number Theory, Springer-Verlag, NewYork—Heidelberg—Berlin, 1981.Google Scholar
5. Hardy, G. H. and Wright, E. M., An Introduction to the Theory of Numbers, (fourth edition), Clarendon Press, Oxford, 1962.Google Scholar