A new estimate of the Montgomery constant in the theory of zeros distribution of the Riemann zeta-function in the critical stripe

{The new value $\alpha=\frac{91}{116}$ is obtained for the constant $\alpha$ such that for all $\sigma\ge\alpha$ the “density hypothesis” is valid for the Riemann zeta-function in the critical stripe. The previous value $\alpha=\frac{11}{14}$ was obtained by M. Jutila in 1977.