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Logarithmic Operators and Characterizations of Completely Multiplicative Functions

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Southeast Asian Bulletin of Mathematics

Abstract

Three logarithmic operators in the ring of arithmetic functions, namely those of Rearick, Carlitz-Subbarao and Shapiro, are considered. Apart from the distinction of values at n = 1, all three logarithms are proved to be essentially the same. Some characterizations of completely multiplicative functions are derived as application.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok, 10900, Thailand

    Vichian Laohakosol

  2. Department of Mathematics, Faculty of Science, The Univ. of the Thai Chamber of Commerce, Bangkok, 10400, Thailand

    Nittiya Pabhapote & Nalinee Wechwiriyakul

Authors
  1. Vichian Laohakosol
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  2. Nittiya Pabhapote
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  3. Nalinee Wechwiriyakul
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Corresponding author

Correspondence to Vichian Laohakosol.

Additional information

This research is partially supported by a 1998-1999 research grant from the University of the Thai Chamber of Commerce.

AMS Mathematics Subject Classification: 11A25

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Laohakosol, V., Pabhapote, N. & Wechwiriyakul, N. Logarithmic Operators and Characterizations of Completely Multiplicative Functions. SEA bull. math. 25, 273–281 (2001). https://doi.org/10.1007/s10012-001-0273-0

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  • DOI: https://doi.org/10.1007/s10012-001-0273-0

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