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On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis

On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis

By using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytic function, we show how an infinite number of integral equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis can be established and p...

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Bibliographic Details
Main Authors: Sekatskii, S.K., Beltraminelli, S., Merlini, D.
Format: Article
Language:English
Published: Інститут математики НАН України 2012
Series:Український математичний журнал
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Online Access:http://dspace.nbuv.gov.ua/handle/123456789/164138
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Summary:By using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytic function, we show how an infinite number of integral equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis can be established and present some of them as an example. It is shown that all earlier known equalities of this type, viz., the Wang equality, Volchkov equality, Balazard–Saias–Yor equality, and an equality established by one of the authors, are certain special cases of our general approach.

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