Improvement of the theorem of Hardy-Littlewood on density of zeros of the function $\zeta(1/2+it)$

Abstract

In this paper we improve classical Hardy-Littlewood exponent $1/2$ by about $16.6\%$ 62 years after the original result. This result is the first step to prove the Selberg's hypothesis (1942). In order to reach our purpose we use discrete method. This paper is the English version of our paper \cite{4}.