Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T02:12:12.462Z Has data issue: false hasContentIssue false
  • English
  • Français

A Multiplicative Analogue of Schur's Tauberian Theorem

Published online by Cambridge University Press:  20 November 2018

Karen Yeats
Karen Yeats*
Affiliation:
Department of Pure Mathematics University of Waterloo Waterloo, Ontario N2L 3G1, e-mail: kayeats@uwaterloo.ca
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.

A theorem concerning the asymptotic behaviour of partial sums of the coefficients of products of Dirichlet series is proved using properties of regularly varying functions. This theorem is a multiplicative analogue of Schur's Tauberian theorem for power series.

Keywords

11N45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 3 , 01 September 2003 , pp. 473 - 480
Copyright
Copyright © Canadian Mathematical Society 2003

References

[1] Apostol, Tom M., Introduction to Analytic Number Theory. Springer-Verlag, New York, 1976.Google Scholar
[2] Bender, Edward A., Asymptotic methods in enumeration. SIAM Rev. 16 (1974), 485–515.Google Scholar
[3] Bingham, N. H., Goldie, C. M. and Teugels, J. L., Regular Variation. Cambridge University Press, Cambridge, 1987.Google Scholar
[4] Burris, Stanley N., Number Theoretic Density and Logical Limit Laws. Math. Surveys Monogr. 86, Amer.Math. Soc., Providence, RI, 2001.Google Scholar
[5] Geluk, J. L. and de Haan, L., Regular variation, extensions and Tauberian theorems. Centrum voor Wiskunde en Informatica, Amsterdam, 1987.Google Scholar
[6] Hardy, G. H. and Riesz, Marcel. The General Theory of Dirichlet's Series. Cambridge University Press, Cambridge, 1952.Google Scholar
[7] Knopfmacher, John, Abstract Analytic Number Theory. North-Holland Mathematical Library 12, North-Holland, Amsterdam, 1975; Available as a Dover Reprint.Google Scholar
[8] Odlyzko, A. M., Asymptotic enumeration methods. Handbook of Combinatorics 1–2, 1063–1229, Elsevier, Amsterdam, 1995.Google Scholar
[9] Pólya, G. and Szegö, G., Aufgaben und Lehrsätze aus der Analysis. I. Springer-Verlag, Berlin, 1970.Google Scholar
[10] Schur, I., Problem:. Arch. Math. Phys. Ser. 3 27(1918), 162.Google Scholar