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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## Details

### 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

- A. Bege, A generalization of von Mangoldt’s function, Bull. Number Theory 14 (1990), 73-78.
- E. Cohen Arithmetical functions associated with arbitrary sets of integers, Acta. Arith. 5 (1959), 407-415.
- E. Cohen, Arithmetical functions associated with the unitary divisors of an integer, Math. Z. 74 (1960), 66-80.
- P. Haukkanen, Some generalized totient functions, Math. Student 56 (1988), 65-74.
- B. Malvina, Trigonometric identities, Intern. J. Math. Math. Sci. 9 (1986), 705-714.
- P. J, McCarthy, Introduction to arithmetical functions, Springer- Verlag, New York, Berlin, Heidelberg, Tokyo, 1986.
- W. Narkiewicz, On a class of arithmetical convolutions, Colloq. Math. 10 (1963), 81-94.
- J. Sandor and L. Toth, A remark on the gamma function, Elem. Math. 44 (1989), 73-76.
- J. Sandor and L. Toth, On some arithmetical products, Publ. Centre Rech. Math. Pures, Serie I., 20 (1990), 5-8.
- V. Sita Ramaiah, Arithmetical sums in regular convolutions, J. Reine Angew. Math. 303/304 (1978), 265-283.
- L. Toth, Contributions to the theory of arithmetical functions defined by regular convolutions (Romanian), thesis, ”Babe§-Bolyai” University, Cluj-Napoca, 1995.
- 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.
- L.Toth, Asymptotic formulae concerning arithmetical functions defined by cross- convolutions, II. The divisor function, Studia Univ. Babe§-Bolyai, Math., to appear.
- 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

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

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

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