On the explicit upper and lower bounds for the number of zeros of the Selberg class

TL;DR

This paper establishes explicit bounds for the error term in the zero-counting formula for the Selberg class, enhancing understanding of zero distribution in the critical strip.

Contribution

It provides the first explicit upper and lower bounds for the zero count error term in the Selberg class, with concrete examples included.

Findings

Explicit bounds for zero count error term derived

Examples illustrating the bounds provided

Improved understanding of zero distribution in the critical strip

Abstract

In this paper we prove explicit upper and lower bounds for the error term in the Riemann-von Mangoldt type formula for the number of zeros inside the critical strip. Furthermore, we also give examples of the bounds.