Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-07-04T22:02:47.503Z Has data issue: false hasContentIssue false
  • English
  • Français

General asymptotic distributions for additive arithmetic functions

Published online by Cambridge University Press:  24 October 2008

P. D. T. A. Elliott
P. D. T. A. Elliott
Affiliation:
University of Colorado, Boulder
Get access Rights & Permissions [Opens in a new window]

Extract

1. Let f(n) be a real-valued additive arithmetic function. Let α(x) and β(x) > 0 be real valued functions, defined for x ≥ 2. Define the frequencies

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 79 , Issue 1 , January 1976 , pp. 43 - 54
Copyright
Copyright © Cambridge Philosophical Society 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Elliott, P. D. T. A.On the limiting distribution of additive arithmetic functions. Acta Math. 132 (1974), 53–75.CrossRefGoogle Scholar
(2)Elliott, P. D. T. A. On the limiting distribution of additive arithmetic functions. II. Logarithmic renormalisation.Google Scholar
(3)Elliott, P. D. T. A.On the law of large numbers for additive arithmetic functions. Math. Proc. Cambridge Philos. Soc. 78 (1975), 33–71.CrossRefGoogle Scholar
(4)Erdös, P. and Kac, M.On the Gaussian law of errors in the theory of additive functions. Proc. Nat. A. Sci. U.S.A. 25 (1939), 206–207.CrossRefGoogle ScholarPubMed
(5)Fainleib, A. S. and Levin, B. V.Application of some integral equations to questions of number theory (Russian). Uspehi Mat. Nauk 22 (135) (1967), 119–197.Google Scholar
(6)Gnedenko, B. V. and Kolmogorov, A. N.Limit distributions for sums of independent random variables (New York; Addison-Wesley, 1954).Google Scholar
(7)Kubilius, J.Probabilistic methods in the theory of numbers. Amer. Math. Soc. Trans. no. 11.Google Scholar
(8)Levin, B. V. and Timofeev, N. M.An analytic method in the probabilistic theory of numbers. Proc. Vladimir Pedag. Inst. Ser. Mat. 38 (1971), 57–150.Google Scholar
(9)Levin, B. V. and Timofeev, N. M.The distribution of additive functions (Russian). Uspehi Mat. Nauk 28 (169) (1973), 243–244.Google Scholar