On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis
Using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytical 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...
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| Date: | 2012 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2012
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/2568 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | Using the generalized Littlewood theorem about a contour integral involving the logarithm of an analytical 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 particular cases of our general approach. |
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