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

• Published in: Український математичний журнал
• Date: 2012
• Main Authors: Sekatskii, S.K., Beltraminelli, S., Merlini, D.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2012
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/164138
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On equalities involving integrals of the logarithm of the Riemann ζ-function and equivalent to the Riemann hypothesis / S.K. Sekatskii, S. Beltraminelli, D. Merlini // Український математичний журнал. — 2012. — Т. 64, № 2. — С. 218-228. — Бібліогр.: 10 назв. — англ.

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...