Skip to main content
Log in

Über eine arithmetische Charakterisierung der multiplikativen, fast-geraden Funktionen

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

Concerning the characterization ofmultiplicative almost-even arithmetical functions (Theorems of ELLIOTT, DABOUSSI, DELANGE) one of the assumptions is weakened. Moreover, counterexamples are given, showing that an exact analogue of the HILDEBRAND-SPILKER characterization ofadditive almost-even functions is not true. Finally two results of SCHWARZ- SPILKER are proved under weaker assumptions.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literatur

  1. H.Daboussi, Caractérisation des fonctions multiplicatives p.p.B λ, Ann.Inst.Fourier (3)30 (1980), 141–166

    Google Scholar 

  2. H.Daboussi,Sur les fonctions multiplicatives ayant une valeur moyenne non nulle, Bull.Soc.Math.France109 (1981), 183–205

    Google Scholar 

  3. P.D.T.A.Elliott,A mean value theorem for multiplicative functions, Proc.London Math.Soc. (3)31 (1975), 418–438

    Google Scholar 

  4. P.D.T.A.Elliott,Mean value theorems for multiplicative functions bounded in mean α-power, α>1, J.Austral.Math.Soc.(A)29 (1980), 177–205

    Google Scholar 

  5. P.D.T.A.Elliott,High-power analogues of the Turán Kubilius inequality, and an application to number theory, Can.Math.J.32 (1980), 893–907

    Google Scholar 

  6. A.Heldebrand undJ.Spilker,Charakterisierung der additiven, fastgeraden Funktionen, Manuscr.Math.32 (1980), 213–230

    Google Scholar 

  7. K.-H.Indlekofer,Some remarks on almost-even and almostperiodic functions, Archiv Math.37 (1981), 353–358

    Google Scholar 

  8. P.Kunth,Einige funktionalanalytische Aspekte in der Theorie der zahlentheoretischen Funktionen, Diss.Univ.Frankfurt, 1988, 101 S.

  9. T.Maxsein,Charakterisierung gewisser Klassen zahlentheoretischer Funktionen, Diss.Univ.Frankfurt, 1985, 70 S.

  10. W.Schwarz,Remarks on the theorem of Elliott and Daboussi, and applications, Proc. 20th Sem.Warszawa (Int.Banach Center Publ.17 (1985), 463–498)

    Google Scholar 

  11. W.Schwarz,A correction to ‘Remarks on Elliott's theorem on mean-values of multiplicative functions’ (Durham 1979/1981) and some remarks on almost-even number-theoretical functions, Sém. Théorie analytique et élémentaire des nombres, Marseille 1983, Publ. Math.Orsay 86-1 (1986), 139–158

  12. W.Schwarz and J.Spilker,Mean values and Ramanujan Expansions of almost even arithmetical functions, Coll.Math.Soc.J.Bolyai13, Topics in Number Theory, Debrecen 1974, 315–357

  13. W.Schwarz and J.Spilker,Remarks on Elliott's theorem on mean- values of multiplicative functions, Recent Progress in Analytic Number Theory, Durham 1979, 325–339 (London 1981)

  14. A.Wintner,Eratosthenian Averages, Baltimore 1943, 81 p.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kunth, P. Über eine arithmetische Charakterisierung der multiplikativen, fast-geraden Funktionen. Manuscripta Math 65, 275–279 (1989). https://doi.org/10.1007/BF01303037

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01303037

Navigation