On the distribution of norms of prime ideals of a given class in arithmetic progressions

Let C be a class of ideals of the ring of algebraic numbers of an imaginary quadratic field. Let l and q be relatively prime integers, , and A₁ τ; 1. An asymptotic formula for the number π₁(x, q, l, C) of prime ideals belonging to the class C whose norms do not exceed x and lie in an arithmetic progression is obtained in this paper. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 322, 2005, pp. 45–62.