The distribution of prime ideals of imaginary quadratic fields

Abstract

Abstract. Let Q(x; y) be a primitive positive definite quadratic form with integer coecients. Then, for all (s; t) 2 R2 there exist (m; n) 2 Z2 such that Q(m; n) is prime and Q(m- s; n - t) Q(s; t)0:53 + 1: This is deduced from another result giving an estimate for the number of prime ideals in an ideal class of an imaginary quadratic number eld that fall in a given sector and whose norm lies in a short interval.