Hostname: page-component-74656f9884-c52kr Total loading time: 0 Render date: 2026-11-08T15:43:35.406Z Has data issue: false hasContentIssue false
  • English
  • Français

On the differences of additive arithmetic functions

Published online by Cambridge University Press:  26 February 2010

P. D. T. A. Elliott
P. D. T. A. Elliott
Affiliation:
University of Colorado, Boulder, Colorado, U.S.A.
Get access

Extract

An arithmetic function f(n) is said to be additive, if it satisfies the relation f(ab) = f(a) + f(b), for every pair of coprime integers a and b; and stronglya dditive if, in addition, f(pm) = f(p) for every prime-power pm.

Information

Type
Research Article
Information
Mathematika , Volume 24 , Issue 2 , December 1977 , pp. 153 - 165
Copyright
Copyright © University College London 1977

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.)

Article purchase

Temporarily unavailable

References

1.Elliott, P. D. T. A.. “On inequalities of Large Sieve type”, Acta Arithmetka, 18 (1971), 405–422.CrossRefGoogle Scholar
2.Elliott, P. D. T. A.. “On connections between the Turan-Kubilius inequality and the large sieve: some applications”, Amer. Math. Soc. Symposia in Pure Math., 24 (1973), 77–82.CrossRefGoogle Scholar
3.Elliott, P. D. T. A.. “A mean-value theorem for multiplicative functions”, Proc. Land. Math. Soc. (3), 31 (1975), 418–438.CrossRefGoogle Scholar
1.Elliott, P. D. T. A.. Probabilistic Number Theory, to be published.Google Scholar
5.Erdős, P.. “On the distribution function of additive functions”, Ann. of Math. (2), 47 (1946), 1–20.CrossRefGoogle Scholar
6.Kátai, I.. “On a problem of P. Erdős”, J. Number Theory, 2 (1970), 1–6.CrossRefGoogle Scholar
7.Kubilius, J.. Probabilistic Methods in the Theory of Numbers. Amer. Math. Soc. Translations of Math. Monographs, Vol. II (Providence, Rhode Island, 1964).Google Scholar
8.Prachar, K.. Primzahlverteilung (Springer, Berlin, 1957).Google Scholar
9.Rinyi, A.. “On a theorem of P. Erdős and its application in information theory”, Mathematica (Cluj), 24 (1959), 341–344.Google Scholar
10.Turán, P.. “On a theorem of Hardy and Ramanujan”, J. Lond. Math. Soc., 9 (1934), 274–276.CrossRefGoogle Scholar
11.Wirsing, E.. Lecture at the Summer Institute on Number Theory. Stony Brook, Long Island (New York, 1964).Google Scholar
12.Wirsing, E. “A characterization of log n as an additive arithmetic function”, Symposia Mathematica dell' Istituto Nazionale di Aha Mathematica, Roma, Vol. IV, 45–57 (Academic Press, London and New York, 1970).Google Scholar