| Title:
|
A generalization of Pillai's arithmetical function involving regular convolutions (English) |
| Author:
|
Tóth, László |
| Language:
|
English |
| Journal:
|
Acta Mathematica et Informatica Universitatis Ostraviensis |
| ISSN:
|
1211-4774 |
| Volume:
|
6 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
203-217 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11A25 |
| MSC:
|
11N37 |
| idZBL:
|
Zbl 1024.11005 |
| idMR:
|
MR1828135 |
| . |
| Date available:
|
2009-01-30T09:07:00Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120534 |
| . |
| Reference:
|
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| Reference:
|
[2] J. Chidambaraswamy R. Sitaramachandrarao: Asymptotic results for a class of arithmetical functions.Monatsh. Math. 99, 1985, pp. 19-27. MR 0778167 |
| Reference:
|
[3] P. Haukkanen: Some generalized totient functions.Math. Student 56, 1988, pp. 65-74. MR 1018263 |
| Reference:
|
[4] P. Haukkanen P. J. McCarthy: Sums of values of even functions.Portugal. Math. 48, 1991, pp. 53-66. MR 1107258 |
| Reference:
|
[5] H. G. Kopetzky: Ein asymptotischer Ausdruck für eine zahlentheoretische Funktion.Monatsh. Math. 84, 1977, pp. 213-217. Zbl 0551.10034, MR 0472735, 10.1007/BF01538032 |
| Reference:
|
[6] P. J. McCarthy: Introduction to arithmetical functions.(1986), Springer-Verlag, New York, Berlin. Zbl 0591.10003, MR 0815514 |
| Reference:
|
[7] W. Narkiewicz: On a class of arithmetical convolutions.Colloq. Math. 10, 1963, pp. 81-94. Zbl 0114.26502, MR 0159778 |
| Reference:
|
[8] S. S. Pillai: On an arithmetic function.J. Annamalai Univ. 2, 1933, pp. 243- 248. Zbl 0008.19603 |
| Reference:
|
[9] V. Sita Ramaiah: Arithmetical sums in regular convolutions.J. Reine Angew. Math. 303/304, 1978, pp. 265-283. Zbl 0391.10007, MR 0514685 |
| Reference:
|
[10] Suryanarayana: Extensions of Dedekind's $\psi$ function.Math. Scand. 26, 1970, pp. 107-118. Zbl 0194.07501, MR 0262188 |
| Reference:
|
[11] L. Tóth: Problem E 3211.Amer. Math. Monthly 94, 1987, p. 457 95; 1988, pp. 962-963. |
| Reference:
|
[12] L. Tóth: An asymptotic formula concerning the unitary divisor sum function.Studia Univ. Babes-Bolyai, Math. 34, 1989, pp. 3-10. MR 1073748 |
| Reference:
|
[13] L. Tóth: The unitary analogue of Pillai's arithmetical function.Collect. Math. 40, 1989, pp. 19-30. Zbl 0712.11010, MR 1078089 |
| Reference:
|
[14] L. Tóth: Some remarks on a generalization of Euler's function.Seminar Arghiriade 23, 1990 9pp. Zbl 0758.11005, MR 1123938 |
| Reference:
|
[15] L. Tóth: The unitary analogue of Pillai's arithmetical function II..Notes Number Theory Discrete Math. 2 yr 1996, pp. 40-46. MR 1418833 |
| Reference:
|
[16] L. Tóth: Asymptotic formulae concerning arithmetical functions defined by cross-convolutions, I. Divisor-sum functions and Euler-type functions.(1997), Math. Debrecen 50, 159-176. MR 1436397 |
| Reference:
|
[17] L. Tóth: Asymptotic formulae concerning arithmetical functions defined by cross-convolutions, II. The divisor function.Studia Univ. Babes-Bolyai, Math., to appear.. MR 2361220 |
| Reference:
|
[18] L. Tóth: Asymptotic formulae concerning arithmetical functions defined by cross-convolutions, III. On the function $\tau_k$.Studia Sci. Math. Hungarica, to appear.. MR 1637588 |
| Reference:
|
[19] L. Tóth: The number and the sum of $P$ - $k$-ary divisors of m which are prime to n.submitted. |
| Reference:
|
[20] L. Tóth P. Haukkanen: A generalization of Euler's $\phi$-function with respect to a set of polynomials.Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 39, 1996, pp. 69-83. MR 1451445 |
| . |
