Skip to main content
SpringerLink
Log in

Multiplicative Functions | g| ≤ 1 and their Convolutions: An Overview

  • Chapter
Book cover Séminaire de Théorie des Nombres, Paris 1987–88

Part of the book series: Progress in Mathematics ((PM,volume 81))

Abstract

In this lecture a multiplicative function g will be defined on the positive integers, assume complex values, and satisfy the relation g(mn) = g(m)g(n) whenever (m,n) = 1. I shall assume that | g(n)| ≤ 1 for all positive n. Overview in the title means that there will be few details, but I will indicate the more important ideas. All the results labelled THEOREM are new, due to myself to appear this year or later.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. H. Delange.- Sur les fonctions arithm00E9tiques multiplicatives de module 2264 1, Acta Arithmetica XLII (1983), 121–151.

    Google Scholar 

  2. P.D.T.A. Elliott - On connections between the Tur00E1n-Kubilius inequality and the Large Sieve: Some applications, Amer. Math. Soc. Proceedings of Symposia in Pure Math., Vol. 24, Providence, 1973, 77–82.

    Google Scholar 

  3. P.D.T.A. Elliott.- Probabilistic Number Theory, I: Mean-Value Theorems, II: Central Limit Theorems, Grund. der Math. Wiss. 239–240, Springer-Verlag, New York, Heidelberg, Berlin, 1979, 1980.

    Google Scholar 

  4. P.D.T.A. Elliott - A new inequality in the theory of additive arithmetic functions, Journ00E9es Arithm00E9tiques (S.M.F.) Colloque Hubert Delange, 7 et 8 juin 1982, Publications Math00E9matiques d’Orsay, Univ. de Paris-Sud.

    Google Scholar 

  5. P.D.T.A. Elliott.- Arithmetic Functions and Integer Product, Grund der Math. Wiss 272, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo (1984/85).

    Google Scholar 

  6. P.D.T.A. Elliott.- Multiplicative functions on arithmetic progressions, Mathematika 34 (1987), 199–206.

    MATH  Google Scholar 

  7. P.D.T.A. Elliott.- Multiplicative functions on arithmetic progressions, II, Mathematika 35 (1988), 38–50.

    MATH  Google Scholar 

  8. G. Halasz.- Uber die Mittelwerte multiplikativer zahlentheoretischer Funktionen, Acta Math. Acad. Sci. Hung. 19 (1968), 365–403.

    Article  MathSciNet  MATH  Google Scholar 

  9. A.Hildebrand- Multiplicative functions in short intervals, Canadian J. Math. 39 (1987), 646–672.

    Article  MathSciNet  MATH  Google Scholar 

  10. Hildebrand- An Erdos-Wintner theorem for differences of additive functions, Preprint, August 26,1987.

    Google Scholar 

  11. E. Wirsing.- Das asymptotische Verhalten von Summen uber multiplikative Funktionen, II, Acta Math. Acad. Sci. Hung. 18 (1967), 411–467.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Colorado, Box 426, Boulder, Colorado, 80309, USA

    P. D. T. A. Elliott

Authors
  1. P. D. T. A. Elliott
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mathématique, Bâtiment 425, Université de Paris-Sud Centre d’Orsay, 91405, Orsay, Cédex, France

    Catherine Goldstein

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Birkhäuser Boston

About this chapter

Cite this chapter

Elliott, P.D.T.A. (1990). Multiplicative Functions | g| ≤ 1 and their Convolutions: An Overview. In: Goldstein, C. (eds) Séminaire de Théorie des Nombres, Paris 1987–88. Progress in Mathematics, vol 81. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3460-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3460-9_4

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8032-3

  • Online ISBN: 978-1-4612-3460-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation