On equalities involving integrals of the logarithm of the Riemann zeta-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 zeta-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.


Published in:
Ukrainian Mathematical Journal, 64, 2, 247-261
Year:
2012
Publisher:
New York, Springer US
ISSN:
0041-5995
Note:
National Licences
Laboratories:




 Record created 2013-02-27, last modified 2019-12-05

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