[[1] ALLOUCHE, J. P.—SHALLIT, J.: Automatic Sequences. Cambridge University Press, Cambridge, 2003.10.1017/CBO9780511546563]Search in Google Scholar
[[2] APOSTOL, T. M.: Modular Functions and Dirichlet Series in Number Theory. In: Graduate Texts in Mathematics Vol. 41 (2nd ed.), Springer-Verlag, Berlin, 1990.]Search in Google Scholar
[[3] BARAT, G.—LIARDET, P.: Dynamical systems originated in the Ostrowski alpha-expansion, Ann. Univ. Sci. Budapest. Sect. Comput. 24, (2004), 133–184.]Search in Google Scholar
[[4] BASSILY, N. L.—KÁTAI, I.: Distribution of the values of q-additive functions on polynomial sequences, Acta Math. Hungar. 68 (1995), no. 4, 353–361.]Search in Google Scholar
[[5] BEREND, D.—KOLESNIK, G.: Joint distribution of completely q-additive functions in residue classes, J. Number Theory 160, (2016), 716–738,10.1016/j.jnt.2015.09.006]Search in Google Scholar
[[6] BERTHÉ, V.: Autour du système de numération d’Ostrowski, Journées Montoises d’Informatique Théorique (Marne-la-Vallée, 2000), Bull. Belg. Math. Soc. Simon Stevin 8 (2001), no. 2, 209–239. In French, with French summary]Search in Google Scholar
[[7] BÉSINEAU, J.: Indépendance statistique d’ensembles liésà la fonction “somme des chiffres”,Acta Arith. 20 (1972), 401–416. (In French)10.4064/aa-20-4-401-416]Search in Google Scholar
[[8] BURGER, E.B.—CLYDE, D. C.—COLBERT, C. H.—SHIN, G. H.—WANG, Z.: A generalization of a theorem of Lekkerkerker to Ostrowski’s decomposition of natural numbers, Acta Arith. 153, (2012), no. 3, 217–249.]Search in Google Scholar
[[9] BUSH, L. E.: An asymptotic formula for the average sum of the digits of integers,Amer. Math. Monthly 47 (1940), 154–156.10.1080/00029890.1940.11990954]Search in Google Scholar
[[10] COQUET, J.—RHIN, G.—TOFFIN, P.: Représentations des entiers naturels et indépendance statistique II, Ann. Inst. Fourier (Grenoble), 31 (1981), no. 1, ix, 1–15. (In French)]Search in Google Scholar
[[11] COQUET, J.—RHIN, G.—TOFFIN, P.: Fourier-Bohr spectrum of sequences related to continued fractions, J. Number Theory 17 (1983), no. 3, 327–336.]Search in Google Scholar
[[12] DARTYGE, C.—TENENBAUM, G.: Sommes des chiffres de multiples d’entiers, Ann. Inst. Fourier (Grenoble), 55 (2005), no. 7, 2423–2474. (In French, with English and French summaries)]Search in Google Scholar
[[13] GEL FOND,A.O.: Sur les nombres qui ont des propriétés additives et multiplicatives données,Acta Arith. 13 (1967/1968), 259–265. (In French)10.4064/aa-13-3-259-265]Search in Google Scholar
[[14] GRAHAM, S. W.—KOLESNIK, G.: Van der Corput’s Method of Exponential Sums. London Mathematical Society Lecture Note Series Vol. 126, In: Cambridge University Press, Cambridge, 1991.]Search in Google Scholar
[[15] KÁTAI, I.—MOGYORÓDI, J.: On the distribution of digits, Publ. Math. Debrecen 15 (1968), 57–68.10.5486/PMD.1968.15.1-4.08]Search in Google Scholar
[[16] KIM, D.-H.: On the joint distribution of q-additive functions in residue classes,J.Number Theory 74 (1999), no. 2, 307–336.]Search in Google Scholar
[[17] KOROBOV, N. M.: Exponential Sums and their Applications. In: Mathematics and its Applications (Soviet Series) Vol. 80, Translated from the 1989 Russian original by Yu. N. Shakhov, Kluwer Academic Publishers Group, Dordrecht, 1992.]Search in Google Scholar
[[18] MAUDUIT, CH.—RIVAT, J.: Sur un problème de Gelfond: la somme des chiffres des nombres premiers, Ann. of Math.(2) 171 (2010), no. 3, 1591–1646. (In: French with English and French summaries)]Search in Google Scholar
[[19] OSTROWSKI, A.: Bemerkungen zur Theorie der Diophantischen Approximationen, Abh. Math. Sem. Univ. Hamburg 1 (1922), no. 1, 77–98. In German]Search in Google Scholar
[[20] SPIEGELHOFER, L.: Correlations for Numeration Systems, PhD Thesis, Vienna, 2014.]Search in Google Scholar
[[21] –––––– Pseudorandomness of the Ostrowski sum-of-digits function, arXiv:1611.03043 [math.NT].]Search in Google Scholar
[[22] VAALER, J. D.: Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. (N.S.), 12, (1985), no. 2, 183–216.]Search in Google Scholar
[[23] ZECKENDORF, E.: Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liège 41 (1972), 179–182. (In French with English summary)]Search in Google Scholar