Remarks on the error term in Chebotarev Density Theorem

TL;DR

This paper examines different effective versions of Chebotarev's density theorem, addressing specific questions posed by Serre and Murty, Murty, and Seradha, to clarify the error terms involved.

Contribution

It provides insights into the error term in Chebotarev's density theorem and responds to open questions from notable mathematicians.

Findings

Clarified the nature of the error term in effective Chebotarev forms

Answered specific open questions posed by Serre and Murty et al.

Enhanced understanding of the theorem's effective bounds

Abstract

We discuss various effective forms of Chebotarev's density theorem, answering a question of Serre and a question of Murty, Murty and Seradha.