Multiplicative functions with small increments. II
Copyright policy )Multiplicative functions with small increments. II
\(\{\) For part I, cf. ibid. 55, No.1/2, 97-101 (1990; Zbl 0709.11050)\(\}\). A complete description is given of the multiplicative functions f that satisfy \[ \sum_{n\leq x}| f(n+K)- f(n)|^{\alpha}=O(\rho^{\alpha}(x)) \] for some K, a constant \(\alpha\geq 1\) and a slowly varying function \(\rho\). Such a function either satisfies \(\sum_{n\leq x}| f(n)| =O(\rho^{\alpha}(x)),\) or it is of the form \(f(n)=n^ su(n)\), where Re \(s\leq 1\) and u is a periodic multiplicative function with period K.
Arithmetic functions in probabilistic number theory, multiplicative functions, mean value, complete description, Asymptotic results on arithmetic functions, small increments, asymptotic property, arithmetic functions, linear recurrence
Arithmetic functions in probabilistic number theory, multiplicative functions, mean value, complete description, Asymptotic results on arithmetic functions, small increments, asymptotic property, arithmetic functions, linear recurrence
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!