On Selberg's theorem C in the theory of the Riemann zeta-function

TL;DR

This paper presents new theorems on exceptional sets related to Selberg's theorem C, using a discrete method that differs from Karatsuba's continuous approach, and includes additional results from previous work.

Contribution

It introduces novel theorems about exceptional sets for Selberg's theorem C using a discrete method not covered by prior continuous theories.

Findings

New theorems about exceptional sets for Selberg's theorem C

Results based on a discrete method distinct from Karatsuba's theory

Additional results from previous related work

Abstract

In this paper we obtain new theorems about classes of exceptional sets for the Selberg's theorem C (1942). Our theorems, as based on discrete method, are not accessible for Karatsuba's theory (1984) since this theory is a continuous theory. This paper is English version of our paper \cite{8}, the results of our paper \cite{9} are added too.