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Periodic, multiplicative number-theoretical functions

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Abstract

D. Leitmann andD. Wolke [3] proved that multiplicative functions, which are restrictions of continuous, periodic functionsF:ℝ→ℂ with irrational period, are constant equal to 0 or 1. In this note a simpler proof for this result is given.

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References

  1. De Bruijn, N. G.: Bijnaperiodicke multiplicatieve functies. Nieuw Archief Wiskunde22, 81–95 (1943).

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  2. Kuipers, L., andH. Niederreiter: Uniform Distribution of Sequences. New York-London-Sydney-Toronto: Wiley-Interscience. 1974.

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  3. Leitmann, D., andD. Wolke: Periodische und multiplikative zahlentheoretische Funktionen. Mh. Math.81, 279–289 (1976).

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Authors and Affiliations

  1. Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, Robert-Mayer-Straße 10, D-6000, Frankfurt am Main 1, Federal Republic of Germany

    Wolfgang Schwarz

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  1. Wolfgang Schwarz
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Schwarz, W. Periodic, multiplicative number-theoretical functions. Monatshefte für Mathematik 87, 65–67 (1979). https://doi.org/10.1007/BF01470938

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  • DOI: https://doi.org/10.1007/BF01470938

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