Some simplest integral equalities equivalent to the Riemann hypothesis

• Datum: 2022
• Hauptverfasser: Sekatskii, S. K., Beltraminelli, S.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2022
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/6222
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

UDC 511.3 We show that the following integral equalities are equivalent to the Riemann hypothesis for any real $a>0$ and any real $0<\epsilon<1,$ $\epsilon \neq 1$:\begin{gather*}\int\limits_{-\infty}^{\infty}\frac{\ln\left(\zeta\left(\dfrac{1}{2}+it\right)\rig...