Expressions for the Dirichlet inverse of arithmetical functions

P. Haukkanen
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 6, 2000, Number 4, Pages 118—124
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P. Haukkanen
Department of Mathematics, Statistics and Philosophy,
FIN-33014 University of Tampere, Finland

Abstract

We express the values of the Dirichlet inverse f -1 in terms of the values of f without using the values of f -1. We use a method based on representing f -1 * f = δ as a system of linear equations. Jagannathan has given many of the results of this paper without proof starting from the basic recurrence relation for the values of f -1.

AMS Classification

  • 11A25

References

  1. M. Aigner, Combinatorial Theory, Springer-Verlag, New York, 1979.
  2. M. G. Beumer, The arithmetical function Tk(N), Amer. Math. Monthly 69 (1962) 777-781.
  3. R. Jagannathan, A matrix approach to certain number theoretic problems, in Proceedings of the Conference on Matrix Algebra, Computational Methods and Number Theory (Mysore, 1976), Matscience Report 87, Institute of Mathematical Sciences, Madras, 1977.
  4. G. Polya and G. Szego, Problems and Theorems in Analysis, Vol. II, Springer- Verlag, 1976.
  5. J.-C. Puclita and J. Spilker, Faltungen von vollstandig multiplikativen Funktio- nen, Arch. Math. 65, No.6 (1995), 516-523.
  6. W. Schwarz and J. Spilker, Arithmetical Functions, London Mathematical Society Lecture Note Series 184, Cambridge University Press, Cambridge, 1994.
  7. R. Sivaramakrishnan, Classical Theory of Arithmetic Functions, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 126, Marcel Dekker, New York, 1989.
  8. R. Vaidyanathaswamy, On the inversion of multiplicative arithmetic functions, J. Indian Math. Soc. (Notes & Questions) 17 (1927), 69-73.

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Cite this paper

APA

Haukkanen, P. (2000). Expressions for the Dirichlet inverse of arithmetical functions. Notes on Number Theory and Discrete Mathematics, 6(4), 118-124.

Chicago

Haukkanen, P. “Expressions for the Dirichlet inverse of arithmetical functions.” Notes on Number Theory and Discrete Mathematics 6, no. 4 (2000): 118-124.

MLA

Haukkanen, P. “Expressions for the Dirichlet inverse of arithmetical functions.” Notes on Number Theory and Discrete Mathematics 6.4 (2000): 118-124. Print.

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