On divisors of sums of integers. V
[Part IV, cf. Can. J. Math. 40, 788-816 (1988; Zbl 0649.10042).] Let \(\omega (n)\) denote the number of distint prime factors of \(n\). The authors estimate both \[ \max_{a\in A,\;b\in B} \omega(a+ b) \quad \text{and} \quad {1\over {|A|\cdot |B|}} \sum_{a\in A,\;b\in B} \omega (a+b) \] for non-empty subsets \(A\) and \(B\) of \(\{1, 2, \dots,N\}\) for which \((|A|\cdot |B|)^{1\over 2}\ll \varepsilon N\). Their explicit results are less suitable for detailed reproduction here.
scientific article; zbMATH DE number 759247