Multiplicative functions with regularity properties. I
Copyright policy )Multiplicative functions with regularity properties. I
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.
- Eötvös Loránd University Hungary
- Centre de Recherche en Informatique France
regularity, completely multiplicative functions, Arithmetic functions; related numbers; inversion formulas, complex valued multiplicative functions, completely multiplicative function, pairs of multiplicative functions, Arithmetic functions in probabilistic number theory, asymptotic recursion relation, multiplicative functions, regularity properties, Applications of sieve methods, Rate of growth of arithmetic functions, Asymptotic results on arithmetic functions
regularity, completely multiplicative functions, Arithmetic functions; related numbers; inversion formulas, complex valued multiplicative functions, completely multiplicative function, pairs of multiplicative functions, Arithmetic functions in probabilistic number theory, asymptotic recursion relation, multiplicative functions, regularity properties, Applications of sieve methods, Rate of growth of arithmetic functions, Asymptotic results on arithmetic functions
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