Multiplicative functions with regularity properties. III (Q795095)

By elementary but rather complicated arguments the author studies those pairs of multiplicative functions f and g for which \(\sum^{\infty}_{n=1}| g(n+K)-f(n)| n^{-1}<\infty\) (K a fixed positive integer) holds. The case \(K=1\) was treated in a former paper of the series [ibid. 43, 105-130 (1984; Zbl 0532.10004)]. In the present paper the problem is solved almost completely for \(K=2\) or K odd.