Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T05:31:31.541Z Has data issue: false hasContentIssue false
  • English
  • Français

On a generalized divisor problem II

Published online by Cambridge University Press:  22 January 2016

Yuk-Kam Lau
Yuk-Kam Lau*
Affiliation:
Institut Élie Cartan, Université Henri Poincaré (Nancy 1), 54506 Vandoeuvre lés Nancy Cedex, France
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.

We investigate the Ω±-result of Δa(x) and its number of sign-changes in an interval [1, T], denoted by Xa(T), for -1 ≤ a < -1/2. We can prove that T ≪aXa(T) which is the best possible in order of magnitude.

Keywords

11N64
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 170 , 2003 , pp. 135 - 143
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

References

[1] Chowla, S., Contributions to the analytic theory of numbers, Math. Z., 35 (1932), 279–299.Google Scholar
[2] Erdös, P. and Shapiro, H.M., On the changes of sign of a certain error function, Canada. J. Math., 3 (1951), 375–385.Google Scholar
[3] Lau, Y.-K., On the mean square formula of the error term for a class of arithmetical function, Mh. Math., 128 (1999), 111–129.CrossRefGoogle Scholar
[4] Lau, Y.-K., On a generalized divisor problem I, Nagoya Math. J., 165 (2002), 71–78.Google Scholar
[5] Lau, Y.-K., On the limiting distribution of a generalized divisor problem for the case -1 ≤ a < -1/2, Acta Arith., 98 (2001), 237–244.Google Scholar
[6] Pétermann, Y.-F. S., Changes of sign of error terms related to Euler’s function and to divisor functions, Comm. Math. Helv., 61 (1986), 84–101.Google Scholar
[7] Pétermann, Y.-F. S., About a Theorem of Paolo Codecà’s and Ω-Estimates for Arithmetical Convolutions, J. Number Theory, 30 (1988), 71–85.CrossRefGoogle Scholar
[8] Pétermann, Y.-F. S., On the distribution of values of an error term related of the Euler functions, Théorie des nombres, (Quebec, PQ, 1987), de Gruyter, Berlin (1989), pp. 785–797.Google Scholar
[9] Pétermann, Y.-F. S., About a Theorem of Paolo Codecà’s and Omega Estimates for Arithmetical Convolutions, Second Part, Ann. Scuola Norm. Sup. Pisa Cl. Sci., (4) 17 (1990), 343–353.Google Scholar