Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-18T21:09:17.775Z Has data issue: false hasContentIssue false
  • English
  • Français

Comportement Asymptotique de

Published online by Cambridge University Press:  20 November 2018

Armel Mercier
Armel Mercier*
Affiliation:
Université du Québec à Chicoutimi Département de Mathématiques 555 Blvd. de l'Université Chicoutimi (Québec) Canada G7H 2B1
Rights & Permissions [Opens in a new window]

Abstract

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.

Let {x} denote the fractional part of x. We find an asymptotic formula of , where k is any positive integer and a is any real number ≥ 1, and so for the sum ∑n<xf(n), where f(n) belongs to a class of additive functions.

Keywords

10H25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 3 , 01 September 1987 , pp. 309 - 317
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Erdös, P. et Alladi, K., On an additive arithmetic function, Pacific Journal of Math 71 (1977), pp. 275–294.Google Scholar
2. Koninck, J. M. De et Ivíc, A., The distribution of the average prime divisor of an integer, Arch. Math. 43 (1984), pp. 37–43.Google Scholar
3. Koninck, J. M. De et Mercier, A., Fonctions arithmétiques tronquées, à paraître.Google Scholar
4. Ferguson, R.P., An application ofStieltjes integration to the power series coefficients of the Riemann zeta function, Amer. Math. Monthly 70 (1963), pp. 60–61.Google Scholar
5. Ishibashi, M. et Kanemitsu, S., On fractional part sums and divisor functions, Proceedings of the Conference on Number Theory, Okayama, Jan. 84.Google Scholar
6. Mercier, A., Sums containing the fractional parts of numbers, Rocky Mountain Journal of Math. 15 (1985), pp. 513–520.Google Scholar
7. Mercier, A. et Nowak, W.G., On the behaviour of sums Monatshefte für Math. 99 (1985), pp. 213–221.Google Scholar
8. Landau, E., Primzahlen, Chelsea Publishing Company.Google Scholar
9. Segal, S.L., On prime-independent additive functions, Archiv der Mathematik 17 (1966), pp. 329–332.Google Scholar