The Iiardy-Littlewood problem for numbers with a fixed number of prime divisors

摘要

In this paper we investigate the number of representations of a natural number N as the sum of a number with k prime divisors and two squares, where k may depend on AT. We determine the asymptotic behaviour when 2≤k≤(2-w) ln ln N and(2 + e) ln ln N≤k≤b ln lnN.