The Large Sieve with Power Moduli in Imaginary Quadratic Number Fields

TL;DR

This paper extends large sieve inequalities to power moduli within imaginary quadratic number fields, broadening the scope of previous results in Gaussian fields and enhancing tools for analytic number theory.

Contribution

It introduces new large sieve inequalities for power moduli in imaginary quadratic fields, generalizing prior work from Gaussian fields.

Findings

Established large sieve inequalities for imaginary quadratic fields.

Extended previous results from Gaussian fields to broader number fields.

Provided new tools for analytic number theory in algebraic settings.

Abstract

We establish large sieve inequalities for power moduli in imaginary quadratic number fields, extending earlier work of Baier and Bansal for the Gaussian field.