On Li's criterion for the Riemann hypothesis for the Selberg class
The author proves a generalization of Li's positivity criterion for the Riemann hypothesis for the extended Selberg class with an Euler sum and obtains two arithmetic expressions for Li's coefficients \(\lambda_F(n)=\sum_\rho\left(1-\left(1-\frac{1}{\rho}\right)^n\right) \) of a function \(F\), where the sum is taken over all non-trivial zeros of \(F\). For related research see \textit{S. Omar} and \textit{K. Mazhouda} [J. Number Theory 125, No. 1, 50--58 (2007; Zbl 1137.11060), J. Number Theory 130, No. 4, 1098--1108 (2010; Zbl 1188.11044), J. Number Theory 130, No. 4, 1109--1114 (2010; Zbl 1188.11045)].
scientific article; zbMATH DE number 5690722
scientific article