On an equality equivalent to the Riemann hypothesis

• Datum: 1995
• Hauptverfasser: Volchkov, V. V., Волчков, В. В.
• Format: Artikel
• Sprache: Russisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 1995
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/5435
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We prove that the Riemann hypothesis on zeros of the zeta function ζ(s) is equivalent to the equality $$\int\limits_0^\infty {\frac{{1 - 12t^2 }}{{(1 + 4t^2 )^3 }}dt} \int\limits_{1/2}^\infty {\ln |\varsigma (\sigma + it)|d\sigma = \pi \frac{{3 - \gamma }}{{32}},}$$ where $$\gamma = \mathop {\li...