2019
Том 71
№ 2

All Issues

Beltraminelli S.

Articles: 1
Article (English)

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

Beltraminelli S., Merlini D., Sekatskii S. K.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 2. - pp. 218-228

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.