On certain arithmetic products involving regular convolutions

László Tóth and József Sándor
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 3, 1997, Number 3, Pages 159—166
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Authors and affiliations

László Tóth
Faculty of Mathematics and Computer Science ”Babes-Bolyai” University
Str. M. Kog & lniccanu 1 RO-3400 Cluj-Napoca Romania

József Sándor
Jud. Harghita RO-4160 Forteni 79 Romania

Abstract

We generalize von Mangoldt’s function and certain arithmetical products of trigonometrical functions and Euler’s gamma, function in terms of Narkiewicz’s regular convolutions. We give arithmetic evaluations for these products and we establish asymptotic formulae for them in case of cross-convolutions, investigated by the first author in previous papers.

Keywords

  • Narkiewicz’s regular convolution
  • Von Mangoldt’s function
  • Euler’s aritmetical function
  • Euler’s gamma function
  • Asymptotic formula

AMS Classification

  • 11A25
  • 11N37
  • 33B15

References

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  8. J. Sandor and L. Toth, A remark on the gamma function, Elem. Math. 44 (1989), 73-76.
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  11. L. Toth, Contributions to the theory of arithmetical functions defined by regular convolutions (Romanian), thesis, ”Babe§-Bolyai” University, Cluj-Napoca, 1995.
  12. L. Toth Asymptotic formulae concerning arithmetical functions defined by crossconvolutions, I. Divisor-sum functions and Euler-type functions, Publ. Math. Debrecen 50 (1997), 159-176.
  13. L.Toth, Asymptotic formulae concerning arithmetical functions defined by cross- convolutions, II. The divisor function, Studia Univ. Babe§-Bolyai, Math., to appear.
  14. L. Toth, Asymptotic formulae concerning arithmetical functions defined by cross- convolutions, III. On the function rk, Studia Sci. Math. Hungarica, to appear.

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Cite this paper

APA

Tóth, L. & Sándor J. (1997). On certain arithmetic products involving regular convolutions. Notes on Number Theory and Discrete Mathematics, 3(3), 159-166.

Chicago

Tóth, László and Sándor József. “On certain arithmetic products involving regular convolutions.” Notes on Number Theory and Discrete Mathematics 3, no. 3 (1997): 159-166.

MLA

Tóth, László and Sándor József. “On certain arithmetic products involving regular convolutions.” Notes on Number Theory and Discrete Mathematics 3.3 (1997): 159-166. Print.

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