A generalization of Pillai's arithmetical function involving regular convolutions

László Tóth

Acta Mathematica et Informatica Universitatis Ostraviensis (1998)

  • Volume: 06, Issue: 1, page 203-217
  • ISSN: 1804-1388

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Tóth, László. "A generalization of Pillai's arithmetical function involving regular convolutions." Acta Mathematica et Informatica Universitatis Ostraviensis 06.1 (1998): 203-217. <http://eudml.org/doc/23813>.

@article{Tóth1998,
author = {Tóth, László},
journal = {Acta Mathematica et Informatica Universitatis Ostraviensis},
keywords = {arithmetic function; convolution},
language = {eng},
number = {1},
pages = {203-217},
publisher = {University of Ostrava},
title = {A generalization of Pillai's arithmetical function involving regular convolutions},
url = {http://eudml.org/doc/23813},
volume = {06},
year = {1998},
}

TY - JOUR
AU - Tóth, László
TI - A generalization of Pillai's arithmetical function involving regular convolutions
JO - Acta Mathematica et Informatica Universitatis Ostraviensis
PY - 1998
PB - University of Ostrava
VL - 06
IS - 1
SP - 203
EP - 217
LA - eng
KW - arithmetic function; convolution
UR - http://eudml.org/doc/23813
ER -

References

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  1. K. Alladi, On generalized Euler functions and related totients, , in New concepts in arithmetic functions, Matscience Report 83, Madras,, 1975. (1975) MR0485656
  2. J. Chidambaraswamy R. Sitaramachandrarao, Asymptotic results for a class of arithmetical functions, Monatsh. Math. 99, 1985, pp. 19-27. (1985) MR0778167
  3. P. Haukkanen, Some generalized totient functions, Math. Student 56, 1988, pp. 65-74. (1988) MR1018263
  4. P. Haukkanen P. J. McCarthy, Sums of values of even functions, Portugal. Math. 48, 1991, pp. 53-66. (1991) MR1107258
  5. H. G. Kopetzky, 10.1007/BF01538032, Monatsh. Math. 84, 1977, pp. 213-217. (1977) Zbl0551.10034MR0472735DOI10.1007/BF01538032
  6. P. J. McCarthy, Introduction to arithmetical functions, (1986), Springer-Verlag, New York, Berlin. (1986) Zbl0591.10003MR0815514
  7. W. Narkiewicz, On a class of arithmetical convolutions, Colloq. Math. 10, 1963, pp. 81-94. (1963) Zbl0114.26502MR0159778
  8. S. S. Pillai, On an arithmetic function, J. Annamalai Univ. 2, 1933, pp. 243- 248. (1933) Zbl0008.19603
  9. V. Sita Ramaiah, Arithmetical sums in regular convolutions, J. Reine Angew. Math. 303/304, 1978, pp. 265-283. (1978) Zbl0391.10007MR0514685
  10. Suryanarayana, Extensions of Dedekind’s ψ function, Math. Scand. 26, 1970, pp. 107-118. (1970) Zbl0194.07501MR0262188
  11. L. Tóth, Problem E 3211, Amer. Math. Monthly 94, 1987, p. 457 95; 1988, pp. 962-963. (1987) 
  12. L. Tóth, An asymptotic formula concerning the unitary divisor sum function, Studia Univ. Babes-Bolyai, Math. 34, 1989, pp. 3-10. (1989) MR1073748
  13. L. Tóth, The unitary analogue of Pillai's arithmetical function, Collect. Math. 40, 1989, pp. 19-30. (1989) Zbl0712.11010MR1078089
  14. L. Tóth, Some remarks on a generalization of Euler's function, Seminar Arghiriade 23, 1990 9pp. (1990) Zbl0758.11005MR1123938
  15. L. Tóth, The unitary analogue of Pillai's arithmetical function II., Notes Number Theory Discrete Math. 2 yr 1996, pp. 40-46. (1996) MR1418833
  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. (1997) MR1436397
  17. L. Tóth, Asymptotic formulae concerning arithmetical functions defined by cross-convolutions, II. The divisor function, Studia Univ. Babes-Bolyai, Math., to appear.. MR2361220
  18. L. Tóth, Asymptotic formulae concerning arithmetical functions defined by cross-convolutions, III. On the function τ k , Studia Sci. Math. Hungarica, to appear.. MR1637588
  19. L. Tóth, The number and the sum of P - k -ary divisors of m which are prime to n, submitted. 
  20. L. Tóth P. Haukkanen, A generalization of Euler’s φ -function with respect to a set of polynomials, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Math. 39, 1996, pp. 69-83. (1996) MR1451445

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