# Conditional upper bound for the k-th prime ideal with given Artin symbol

## TL;DR

This paper establishes an explicit upper bound for the k-th prime ideal with a specified Artin symbol, assuming the Riemann hypothesis for Dedekind zeta functions, advancing understanding of prime distribution in number fields.

## Contribution

It provides a new explicit upper bound for prime ideals with a given Artin symbol under the Riemann hypothesis, linking prime ideal distribution to analytic number theory.

## Key findings

- Derived an explicit upper bound for the k-th prime ideal with fixed Artin symbol
- Assumed the Riemann hypothesis for Dedekind zeta functions to obtain results
- Enhanced understanding of prime ideal distribution in algebraic number fields

## Abstract

We prove an explicit upper bound for the k-th prime ideal with fixed Artin symbol, under the assumption of the validity of the Riemann hypothesis for the Dedekind zeta functions.