Completely q-multiplicative functions: the Mellin transform approach

Peter J. Grabner

Acta Arithmetica (1993)

  • Volume: 65, Issue: 1, page 85-96
  • ISSN: 0065-1036

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Peter J. Grabner. "Completely q-multiplicative functions: the Mellin transform approach." Acta Arithmetica 65.1 (1993): 85-96. <http://eudml.org/doc/206564>.

@article{PeterJ1993,
author = {Peter J. Grabner},
journal = {Acta Arithmetica},
keywords = {completely -multiplicative functions; digit expansion; summatory function; Mellin transform; Dirichlet generating function; Hausdorff measure},
language = {eng},
number = {1},
pages = {85-96},
title = {Completely q-multiplicative functions: the Mellin transform approach},
url = {http://eudml.org/doc/206564},
volume = {65},
year = {1993},
}

TY - JOUR
AU - Peter J. Grabner
TI - Completely q-multiplicative functions: the Mellin transform approach
JO - Acta Arithmetica
PY - 1993
VL - 65
IS - 1
SP - 85
EP - 96
LA - eng
KW - completely -multiplicative functions; digit expansion; summatory function; Mellin transform; Dirichlet generating function; Hausdorff measure
UR - http://eudml.org/doc/206564
ER -

References

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  1. [Al87] J.-P. Allouche, Automates finis en théorie des nombres, Exposition. Math. 5 (1987), 239-266. Zbl0641.10041
  2. [AC85] J.-P. Allouche and H. Cohen, Dirichlet series and curious infinite products, Bull. London Math. Soc. 17 (1985), 531-538. Zbl0577.10036
  3. [AS88] J.-P. Allouche and J. O. Shallit, Sums of digits and the Hurwitz zeta function, in: Analytic Number Theory, Lecture Notes in Math. 1434, Sprin- ger, Berlin, 1988, 19-30. 
  4. [Ap84] T. M. Apostol, Introduction to Analytic Number Theory, Springer, Berlin, 1984. 
  5. [Co83] J. Coquet, A summation formula related to the binary digits, Invent. Math. 73 (1983), 107-115. Zbl0528.10006
  6. [De72] H. Delange, Sur les fonctions q-additives ou q-multiplicatives, Acta Arith. 21 (1972), 285-298. Zbl0219.10062
  7. [De75] H. Delange, Sur la fonction sommatoire de la fonction ``Somme des Chiffres'', Enseign. Math. (2) 21 (1975), 31-47. Zbl0306.10005
  8. [Du83] J.-M. Dumont, Discrépance des progressions arithmétiques dans la suite de Morse, C. R. Acad. Sci. Paris 297 (1983), 145-148. 
  9. [FGKPT92] P. Flajolet, P. J. Grabner, P. Kirschenhofer, H. Prodinger and R. F. Tichy, Mellin transforms and asymptotics: digital sums, Theoret. Comput. Sci. (to appear). Zbl0788.44004
  10. [FRS85] P. Flajolet, M. Regnier and R. Sedgewick, Some uses of the Mellin integral transform in the analysis of algorithms, in: Combinatorial Algorithms on Words, A. Apostolico and Z. Galil (eds.), Springer, Berlin, 1985, 241-254. Zbl0582.68015
  11. [Ge68] A. O. Gelfond, Sur les nombres qui ont des propriétés additives et multiplicatives données, Acta Arith. 13 (1968), 259-266. Zbl0155.09003
  12. [GKS92] S. Goldstein, K. A. Kelly and E. R. Speer, The fractal structure of rarefied sums of the Thue-Morse sequence, J. Number Theory 42 (1992), 1-19. Zbl0788.11010
  13. [Gr93] P. J. Grabner, A note on the parity of the sum-of-digits function, manu- script. 
  14. [Ha77] H. Harborth, Number of odd binomial coefficients, Proc. Amer. Math. Soc. 62 (1977), 19-22. Zbl0323.10043
  15. [HR15] G. H. Hardy and M. Riesz, The General Theory of Dirichlet's Series, Cambridge University Press, 1915. Zbl45.0387.03
  16. [Ma29] K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366. Zbl55.0115.01
  17. [MM83] J.-L. Mauclaire and L. Murata, On q-additive functions, II, Proc. Japan Acad. 59 (1983), 441-444. Zbl0541.10040
  18. [Ne69] D. J. Newman, On the number of binary digits in a multiple of three, Bull. Amer. Math. Soc. 21 (1969), 719-721. Zbl0194.35004
  19. [St89] A. H. Stein, Exponential sums of digit counting functions, in: Théorie des nombres, Comptes Rendus de la Conférence Internationale de Théorie des Nombres tenue à l'Université Laval en 1987, J. M. De Koninck and C. Levesque (eds.), W. de Gruyter, Berlin, 1989, 861-868. 
  20. [Sto77] K. B. Stolarsky, Power and exponential sums of digital sums related to binomial coefficient parity, SIAM J. Appl. Math. 32 (1977), 717-730 Zbl0355.10012

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