Gaussian almost primes in almost all narrow sectors

Abstract

We show that almost all sectors of the disc {z is an element of C : vertical bar z vertical bar(2) <= X} of area (log X)(15.1) contain products of exactly two Gaussian primes, and that almost all sectors of area (log X)(1+epsilon) contain products of exactly three Gaussian primes. The argument is based on mean value theorems, large value estimates and pointwise bounds for Hecke character sums.