Generalized Bombieri–Lagarias’ Theorem and Generalized Li’s Criterion with its Arithmetic Interpretation

• Date: 2014
• Main Authors: Sekatskii, S. K., Секацький, С.К.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2014
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2139
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We show that Li’s criterion equivalent to the Riemann hypothesis, i.e., the statement that the sums $$ {k}_n={\Sigma}_{\rho}\left(1-{\left(1-\frac{1}{\rho}\right)}^n\right) $$ over zeros of the Riemann xi-function and the derivatives $$ \begin{array}{ccc}\hfill {\lambda}_n\equiv \frac{1}{\left(n-...