Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH, II

TL;DR

This paper presents an improved explicit version of the prime ideal theorem under GRH with optimal asymptotic behavior, advancing the understanding of prime distribution in number fields.

Contribution

It provides a new explicit formulation of the prime ideal theorem under GRH with optimal asymptotic properties, improving previous results.

Findings

Achieved an explicit version with optimal asymptotic behavior

Enhanced understanding of prime distribution under GRH

Refined bounds in the prime ideal theorem

Abstract

We have proved recently several explicit versions of the prime ideal theorem under GRH. Here we prove a version with optimal asymptotic behaviour.