The asymptotic estimation of prime ideals in imaginary quadratic fields and Chebyshev's bias

TL;DR

This paper investigates the asymptotic behavior of prime ideals in imaginary quadratic fields under specific conditions and explores Chebyshev's bias in their distribution across residue classes.

Contribution

It provides new asymptotic estimates for prime ideals in imaginary quadratic fields and analyzes Chebyshev's bias in their distribution.

Findings

Derived asymptotic formulas for prime ideals with certain properties

Identified biases in the distribution of prime ideals among residue classes

Enhanced understanding of prime ideal distribution in quadratic fields

Abstract

We study the asymptotic estimation of prime ideals that satisfy certain congruence and argument conditions in imaginary quadratic fields. We also discuss the phenomenon of Chebyshev's bias in the distribution of prime ideals among different residue classes.