Abstract
Let f(n) be a real-valued additive arithmetic function. In Chapters 13 and 14 we discussed when the frequencies
may converge to the improper law, assuming only that β(x) does not increase too rapidly. In the present chapter we strengthen somewhat this assumption concerning β(x), and consider their possible convergence to laws more general than the improper law. In particular, we shall show that every stable law may occur as a limit law. We make use of the results of Chapter 14, but not of its method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1980 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Elliott, P.D.T.A. (1980). General Laws for Additive Functions. I: Including the Stable Laws. In: Probabilistic Number Theory II. Grundlehren der mathematischen Wissenschaften, vol 240. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9992-9_6
Download citation
DOI: https://doi.org/10.1007/978-1-4612-9992-9_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9994-3
Online ISBN: 978-1-4612-9992-9
eBook Packages: Springer Book Archive