Skip to main content

On some arithmetic convolutions

  • Conference paper
  • First Online:
The Theory of Arithmetic Functions

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 251))

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. T. Bell, On Liouville's theorems concerning certain numerical functions, Bull. Amer. Math. Soc. 19 (1912), 164–166.

    Google Scholar 

  2. E. T. Bell, Euler Algebra, Trans. Amer. Math. Soc. 25 (1923), 135–154.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. T. Bell, Outline of a theory of arithmetical functions in their algebraic aspects, J. Indian Math. Soc. 17 (1928), 249–260.

    MATH  Google Scholar 

  4. E. T. Bell, Factorability of numerical functions, Bull. Amer. Math. Soc. 37 (1931), 251–253.

    Article  MathSciNet  MATH  Google Scholar 

  5. L. Carlitz, Rings of arithmetic functions, Pacific J. Math. 14 (1964), 1165–1171.

    Article  MathSciNet  MATH  Google Scholar 

  6. L. Carlitz, Arithmetic functions in an unusual setting, Amer. Math.Monthly 73 (1966), 582–590.

    Article  MathSciNet  MATH  Google Scholar 

  7. L. Carlitz, Arithmetical functions in an unusual setting II, Duke Math. J. 34 (1967), 757–759.

    Article  MathSciNet  MATH  Google Scholar 

  8. E. D. Cashwell and C. J. Everett, The ring of number-theoretic functions, Pacific J. Math. 9 (1959), 975–985.

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Chidambaraswamy, Sum functions of unitary and semi-unitary divisors, J. Indian Math. Soc. 31 (1967), 117–126.

    MathSciNet  MATH  Google Scholar 

  10. E. Cohen, Rings of arithmetic functions, Duke Math. J. 19 (1952), 115–129.

    Article  MathSciNet  MATH  Google Scholar 

  11. E. Cohen, Rings of arithmetic functions II: The number of solutions of quadratic congruences, Duke Math. J. 21 (1954), 9–28.

    Article  MathSciNet  MATH  Google Scholar 

  12. E. Cohen, Unitary products of arithmetical functions, Acta Arith. 7 (1961), 29–38.

    MathSciNet  MATH  Google Scholar 

  13. E. Cohen, Arithmetical functions of finite Abelian groups, Math. Ann. 142 (1961), 165–182.

    Article  MathSciNet  MATH  Google Scholar 

  14. H. H. Crapo, The Möbius function of a lattice, J. Combinatorial Theory 1 (1966), 126–131.

    Article  MathSciNet  MATH  Google Scholar 

  15. T. M. K. Davison, On arithmetic convolutions, Canad. Math. Bull. 9 (1966), 287–296.

    Article  MathSciNet  MATH  Google Scholar 

  16. H. Delange, Sur certaines functions additives á valeur entiers, Acta Arith. 16 (1969/70), 195–206.

    MathSciNet  MATH  Google Scholar 

  17. P. Erdös, (Private communication to the author).

    Google Scholar 

  18. G. Gesely, A generalized arithmetic composition, Amer. Math. Monthly 74 (1967), 1216–1217.

    Article  MathSciNet  Google Scholar 

  19. A. A. Gioia, The k-product of arithmetic functions, Canad. J. Math. 17 (1965), 970–976.

    Article  MathSciNet  MATH  Google Scholar 

  20. A. A. Gioia, On an identity for multiplicative functions, Amer. Math. Monthly 69 (1962), 988–991.

    Article  MathSciNet  MATH  Google Scholar 

  21. A. A. Gioia, Generalized Dirichlet products of number theoretic functions. Ph.D. Thesis, University of Missouri, 1964.

    Google Scholar 

  22. D. L. Goldsmith, On the multiplicative properties of arithmetic functions, Pacific J. Math. 27 (1968), 283–304.

    Article  MathSciNet  MATH  Google Scholar 

  23. D. L. Goldsmith, A generalized convolution for arithmetic functions, Duke Math. J. 38 (1971), 279–283.

    Article  MathSciNet  MATH  Google Scholar 

  24. D. H. Lehmer, Arithmetic of double series, Trans. Amer. Math. Soc. 33 (1931), 945–457.

    Article  MathSciNet  MATH  Google Scholar 

  25. D. H. Lehmer, A new calculus of numerical functions, Amer. J. Math. 53 (1931), 843–854.

    Article  MathSciNet  MATH  Google Scholar 

  26. D. H. Lehmer, Polynomials for the n-ary composition of numerical functions, Amer. J. Math. 58 (1936), 563–572.

    Article  MathSciNet  MATH  Google Scholar 

  27. P. J. McCarthy, Regular arithmetical convolutions, Portugal. Math. 10 (1963), 81–94.

    Google Scholar 

  28. W. Narkiewicz, On a class of arithmetical convolutions, Colloq. Math. 10 (1963), 81–94.

    MathSciNet  MATH  Google Scholar 

  29. J. Popken, On convolutions in number theory, Indag. Math. 17 (1955), 10–15.

    Article  MathSciNet  MATH  Google Scholar 

  30. D. Rearick, Semi multiplicative functions, Duke Math. J. 33 (1966), 49–54.

    Article  MathSciNet  MATH  Google Scholar 

  31. D. Rearick, Operations on algebras of arithmetic functions, Duke Math. J. 35 (1968), 761–766.

    Article  MathSciNet  MATH  Google Scholar 

  32. G. C. Rota, On the foundations of combinatorial theory I. Theory of Möbius functions, Z. Wahrscheinlichkeitstheorie und Verw. 2 (1964), 340–368.

    Article  MathSciNet  MATH  Google Scholar 

  33. R. Siva Ramakrishna, Contributions to the study of multiplicative arithmetic functions, (to appear).

    Google Scholar 

  34. V. Sivaramprasad and D. Suryanarayana, Sum functions of k-ary and semi-k-ary divisors, J. Austral. Math. Soc. (to appear).

    Google Scholar 

  35. D. A. Smith, Incidence functions as generalized arithmetic functions I, Duke Math. J. 34 (1967), 617–633.

    Article  MathSciNet  MATH  Google Scholar 

  36. D. A. Smith, Incidence functions as generalized arithmetic functions II, Duke Math. J. 36 (1969), 15–30.

    Article  MathSciNet  MATH  Google Scholar 

  37. D. A. Smith, Incidence functions as generalized arithmetic functions III, Duke Math. J. 36 (1969), 353–367.

    Article  MathSciNet  MATH  Google Scholar 

  38. M. V. Subbarao and A. A. Gioia, Generalized Dirichlet products of arithmetical functions (abstract), Notices Amer. Math. Soc. 10 (1963), No. 7, p. 661.

    Google Scholar 

  39. M. V. Subbarao and A. A. Gioia, Identities for multiplicative functions, Canad. Math. Bull. 10 (1967), 65–73.

    Article  MathSciNet  MATH  Google Scholar 

  40. M. Sugunamma, Contributions to the study of general arithmetic functions, Ph.D. Thesis, Sri Venkateswara University, Tirupati, India, 1965.

    Google Scholar 

  41. D. Suryanarayana, The number of bi-unitary divisors of an integer, Proceedings of a Conference on the Theory of Arithmetic Functions, Kalamazoo, 1971.

    Google Scholar 

  42. R. Vaidyanathaswamy, The identical equations of the multiplicative function, Bull. Amer. Math. Soc. 36 (1930), 762–772.

    Article  MathSciNet  MATH  Google Scholar 

  43. R. Vaidyanathaswamy, The theory of multiplicative arithmetical functions, Trans. Amer. Math. Soc. 33 (1931), 579–662.

    Article  MathSciNet  MATH  Google Scholar 

  44. L. Weisner, Abstract theory of inversion of finite series, Trans. Amer. Math. Soc. 38 (1935), 474–484.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Anthony A. Gioia Donald L. Goldsmith

Rights and permissions

Reprints and permissions

Copyright information

© 1972 Springer-Verlag

About this paper

Cite this paper

Subbarao, M.V. (1972). On some arithmetic convolutions. In: Gioia, A.A., Goldsmith, D.L. (eds) The Theory of Arithmetic Functions. Lecture Notes in Mathematics, vol 251. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058796

Download citation

  • DOI: https://doi.org/10.1007/BFb0058796

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05723-9

  • Online ISBN: 978-3-540-37098-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics