@article{bwmeta1.element.bwnjournal-article-aav65i1p85bwm, author = {Peter J. Grabner}, title = {Completely q-multiplicative functions: the Mellin transform approach}, journal = {Acta Arithmetica}, volume = {64}, year = {1993}, pages = {85-96}, zbl = {0783.11035}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav65i1p85bwm} }
Peter J. Grabner. Completely q-multiplicative functions: the Mellin transform approach. Acta Arithmetica, Tome 64 (1993) pp. 85-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav65i1p85bwm/
[000] [Al87] J.-P. Allouche, Automates finis en théorie des nombres, Exposition. Math. 5 (1987), 239-266. | Zbl 0641.10041
[001] [AC85] J.-P. Allouche and H. Cohen, Dirichlet series and curious infinite products, Bull. London Math. Soc. 17 (1985), 531-538. | Zbl 0577.10036
[002] [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.
[003] [Ap84] T. M. Apostol, Introduction to Analytic Number Theory, Springer, Berlin, 1984.
[004] [Co83] J. Coquet, A summation formula related to the binary digits, Invent. Math. 73 (1983), 107-115. | Zbl 0528.10006
[005] [De72] H. Delange, Sur les fonctions q-additives ou q-multiplicatives, Acta Arith. 21 (1972), 285-298. | Zbl 0219.10062
[006] [De75] H. Delange, Sur la fonction sommatoire de la fonction ``Somme des Chiffres'', Enseign. Math. (2) 21 (1975), 31-47. | Zbl 0306.10005
[007] [Du83] J.-M. Dumont, Discrépance des progressions arithmétiques dans la suite de Morse, C. R. Acad. Sci. Paris 297 (1983), 145-148.
[008] [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). | Zbl 0788.44004
[009] [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. | Zbl 0582.68015
[010] [Ge68] A. O. Gelfond, Sur les nombres qui ont des propriétés additives et multiplicatives données, Acta Arith. 13 (1968), 259-266. | Zbl 0155.09003
[011] [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. | Zbl 0788.11010
[012] [Gr93] P. J. Grabner, A note on the parity of the sum-of-digits function, manu- script.
[013] [Ha77] H. Harborth, Number of odd binomial coefficients, Proc. Amer. Math. Soc. 62 (1977), 19-22. | Zbl 0323.10043
[014] [HR15] G. H. Hardy and M. Riesz, The General Theory of Dirichlet's Series, Cambridge University Press, 1915. | Zbl 45.0387.03
[015] [Ma29] K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366. | Zbl 55.0115.01
[016] [MM83] J.-L. Mauclaire and L. Murata, On q-additive functions, II, Proc. Japan Acad. 59 (1983), 441-444. | Zbl 0541.10040
[017] [Ne69] D. J. Newman, On the number of binary digits in a multiple of three, Bull. Amer. Math. Soc. 21 (1969), 719-721. | Zbl 0194.35004
[018] [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.
[019] [Sto77] K. B. Stolarsky, Power and exponential sums of digital sums related to binomial coefficient parity, SIAM J. Appl. Math. 32 (1977), 717-730 | Zbl 0355.10012