Basic properties of weakly multiplicative functions

Pentti Haukkanen
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 8, 2002, Number 2, Pages 70—74
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Authors and affiliations

Pentti Haukkanen
Department of Mathematics, Statistics and Philosophy
FIN-33014 University of Tampere, Finland

Abstract

An arithmetical function f is said to be weakly multiplicative if f is not identically zero and f(np) = f(n)f(p) for all positive integers n and primes p with (n, p) = 1. Every multiplicative function is a weakly multiplicative function but the converse is not true. In this note we study basic properties of weakly multiplicative functions with respect to the Dirichlet convolution.

AMS Classification

  • 11A25

References

  1. T. M. Apostol. Introduction to Analytic Number Theory. UTM. New York: Springer-Verlag, 1976.
  2. I. Katai & M. V. Subbarao. “Quasi-additive and quasi-multiplicative functions with regularity properties.” Publ. Math. 56 (2000): 43-52.
  3. P. J. McCarthy. Introduction to Arithmetical Functions. Universitext. New York: Springer-Verlag, 1986.
  4. R. Sivaramakrishnan. Classical Theory of Arithmetic Functions. Monographs and Textbooks in Pure and Applied Mathematics, Vol. 126. New York: Marcel Dekker, Inc., 1989.

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Cite this paper

APA

Haukkanen, P. (2002). Basic properties of weakly multiplicative functions. Notes on Number Theory and Discrete Mathematics, 8(2), 70-74.

Chicago

Haukkanen, Pentti. “Basic Properties of Weakly Multiplicative Functions.” Notes on Number Theory and Discrete Mathematics 8, no. 2 (2002): 70-74.

MLA

Haukkanen, Pentti. “Basic Properties of Weakly Multiplicative Functions.” Notes on Number Theory and Discrete Mathematics 8.2 (2002): 70-74. Print.

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