Download PDF - Completely q-multiplicative functions: the Mellin transform approachAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Completely q-multiplicative functions: the Mellin transform approach

Authors 1

Affiliations

  1. Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria

Bibliography

  1. [Al87] J.-P. Allouche, Automates finis en théorie des nombres, Exposition. Math. 5 (1987), 239-266.
  2. [AC85] J.-P. Allouche and H. Cohen, Dirichlet series and curious infinite products, Bull. London Math. Soc. 17 (1985), 531-538.
  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.
  6. [De72] H. Delange, Sur les fonctions q-additives ou q-multiplicatives, Acta Arith. 21 (1972), 285-298.
  7. [De75] H. Delange, Sur la fonction sommatoire de la fonction ``Somme des Chiffres'', Enseign. Math. (2) 21 (1975), 31-47.
  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).
  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.
  11. [Ge68] A. O. Gelfond, Sur les nombres qui ont des propriétés additives et multiplicatives données, Acta Arith. 13 (1968), 259-266.
  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.
  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.
  15. [HR15] G. H. Hardy and M. Riesz, The General Theory of Dirichlet's Series, Cambridge University Press, 1915.
  16. [Ma29] K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366.
  17. [MM83] J.-L. Mauclaire and L. Murata, On q-additive functions, II, Proc. Japan Acad. 59 (1983), 441-444.
  18. [Ne69] D. J. Newman, On the number of binary digits in a multiple of three, Bull. Amer. Math. Soc. 21 (1969), 719-721.
  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
Acta Arithmetica
1993/65/1
Export to PBN, Opens in new tab
Pages:
85-96
Main language of publication
English
Received
1992-07-14
Accepted
1993-03-22
Published
1993
Exact and natural sciences