Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-26T16:16:06.243Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiplicative Functions in Short Intervals

Published online by Cambridge University Press:  20 November 2018

Adolf Hildebrand
Adolf Hildebrand*
Affiliation:
University of Illinois, Urbana, Illinois
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A central problem in probabilistic number theory is to evaluate asymptotically the partial sums

of multiplicative functions f and, in particular, to find conditions for the existence of the “mean value”

1.1

In the last two decades considerable progress has been made on this problem, and the results obtained are very satisfactory.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 3 , 01 June 1987 , pp. 646 - 672
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Babu, G. J., Probabilistic methods in the theory of arithmetical functions, Macmillan Lectures in Mathematics, New Delhi (1978).Google Scholar
2. Babu, G. J., On the distribution of arithmetic functions, Acta Arith. 29 (1976), 97–104.Google Scholar
3. Babu, G. J., On the mean values and distributions of arithmetic functions, Acta Arith. 40 (1981), 63–77.Google Scholar
4. Delange, H., Sur les fonctions arithmétiques multiplicatives, Ann. Scient. Ec. Norm. Sup. 75 (1961), 273–304.Google Scholar
5. Elliott, P. D. T. A., Probabilistic number theory I, II (Springer, New York, 1979, 1980).CrossRefGoogle Scholar
6. Elliott, P. D. T. A., Arithmetic functions and integer products (Springer, New York, 1985).CrossRefGoogle Scholar
7. Halá;sz, G., Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen, Acta Math. Acad. Sci. Hung. 19 (1968), 365–403.Google Scholar
8. Halá;sz, G., On the distribution of additive arithmetic functions. Acta Arith. 27 (1975), 143–152.Google Scholar
9. Halberstam, H. and Richert, H.-E., On a result of R. R. Hall, J. Number Theory 11 (1979), 76–89.Google Scholar
10. Hildebrand, A., On Wirsing's mean value theorem for multiplicative functions, Bull. London Math Soc. 18 (1986), 147–152.Google Scholar
11. Huxley, M. N., On the difference between consecutive primes, Invent. Math. 15 (1972), 164–170.Google Scholar
12. Montgomery, H. L., A note on mean values of multiplicative functions, Preprint. Mittag-Leffler Institute (1978).Google Scholar
13. Motohashi, Y., On the sum of the Môbiusfunction in a short segment, Proc. Japan Acad. 52 (1976), 477–479.Google Scholar
14. Ramachandra, K., Some problems of analytic number theory, Acta Arith. 31 (1976), 313–323.Google Scholar
15. Shiu, P., A Brun-Titchmarsh theorem for multiplicative functions, J. Reine Ang. Math. 313 (1980), 161–170.Google Scholar
16. Wirsing, E., Das asymptotische Verhalten von Summen über multiplikative Funktionen II, Acta Math. Acad. Sci. Hung. 18 (1967), 411–467.Google Scholar