The large sieve with power moduli in imaginary quadratic number fields

Abstract

In this paper, we establish large sieve inequalities for power moduli in imaginary quadratic number fields, extending earlier work of Baier and Bansal [S. Baier and A. Bansal, The large sieve with power moduli for [Formula: see text], Int. J. Number Theory 14 (10) (2018) 2737–2756; Large sieve with sparse sets of moduli for [Formula: see text], Acta Arith. 196 (1) (2020) 17–34] for the Gaussian field.