Distribution properties of digital expansions arising from linear recurrences
Mathematica slovaca, Tome 53 (2003) no. 1, pp. 1-20

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR   Zbl

Classification : 11B37, 11K16, 11L07
Lamberger, Mario; Thuswaldner, Jörg M. Distribution properties of digital expansions arising from linear recurrences. Mathematica slovaca, Tome 53 (2003) no. 1, pp. 1-20. http://geodesic.mathdoc.fr/item/MASLO_2003_53_1_a0/
@article{MASLO_2003_53_1_a0,
     author = {Lamberger, Mario and Thuswaldner, J\"org M.},
     title = {Distribution properties of digital expansions arising from linear recurrences},
     journal = {Mathematica slovaca},
     pages = {1--20},
     year = {2003},
     volume = {53},
     number = {1},
     mrnumber = {1964200},
     zbl = {1048.11066},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MASLO_2003_53_1_a0/}
}
TY  - JOUR
AU  - Lamberger, Mario
AU  - Thuswaldner, Jörg M.
TI  - Distribution properties of digital expansions arising from linear recurrences
JO  - Mathematica slovaca
PY  - 2003
SP  - 1
EP  - 20
VL  - 53
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MASLO_2003_53_1_a0/
LA  - en
ID  - MASLO_2003_53_1_a0
ER  - 
%0 Journal Article
%A Lamberger, Mario
%A Thuswaldner, Jörg M.
%T Distribution properties of digital expansions arising from linear recurrences
%J Mathematica slovaca
%D 2003
%P 1-20
%V 53
%N 1
%U http://geodesic.mathdoc.fr/item/MASLO_2003_53_1_a0/
%G en
%F MASLO_2003_53_1_a0

[1] BRAUER A.: On algebraic equations with all but one root in the interior of the unit circle. Math. Nachr. 4 (1951), 250-257. | MR | Zbl

[2] COQUET J.-RHIN G.-TOFFIN P.: Représentation des entiers naturels et indépendence statistique 2. Ann. Inst. Fourier (Grenoble) 31 (1981), 1-15. | MR

[3] DELANGE H.: Sur la fonction sommatoire de la fonction "somme des chiffres". Enseign. Math. (2) 21 (1975), 31-47. | MR | Zbl

[4] DRMOTA M.-GAJDOSIK J.: The distribution of the sum-of-digits function. J. Théor. Nombres Bordeaux 10 (1998), 17-32. | MR | Zbl

[5] DRMOTA M.-GAJDOSIK J.: The parity of the sum-of-digits-function of generalized zeckendorf representations. Fibonacci Quart 36 (1998), 3-19. | MR | Zbl

[6] DUMONT J. M.-SIDOROV N.-THOMAS A.: Number of representations related to a linear recurrent basis. Acta Arith. 88 (1999), 371-396. | MR | Zbl

[7] DUMONT J. M.-THOMAS A.: Digital sum moments and substitutions. Acta Arith. 64 (1993), 205-225. | MR | Zbl

[8] DUMONT J. M.-THOMAS A.: Gaussian asymptotic properties of the sum-of-digits function. J. Number Theory 62 (1997), 19-38. | MR | Zbl

[9] FINE N. J.: The distribution of the sum of digits (mod p). Bull. Amer. Math. Soc. 71 (1965), 651-652. | MR | Zbl

[10] FOUVRY E.-MAUDUIT C.: Sommes des chiffres et nombres presque premiers. Math. Ann. 305 (1996), 571-599. | MR | Zbl

[11] FROUGNY C.: Representations of numbers and finite automata. Math. Systems Theory 25 (1992), 37-60. | MR | Zbl

[12] GEL'FOND A. O.: Sur les nombres qui ont des proprietes additives et multiplicatives donnees. Acta Arith. 13 (1968), 259-265. | MR

[13] GRABNER P.-TICHY R.: Contributions to digit expansions with respect to linear recurrences. J. Number Theory 36 (1990), 160-169. | MR | Zbl

[14] GRABNER P. J.: Ziffernentwicklungen bezuglich linearer Rekursionen. Anz. Osterreich.Akad. Wiss Math.-Natur. Kl. 1990 (1990), 1-21. | MR

[15] GRABNER P. J.-TICHY R. F.: \alpha$-expansions, linear recurrences, and the sum-of-digits function. Manuscripta Math. 70 (1991), 311-324. | MR | Zbl

[16] HOIT A.: The distribution of generalized sum-of-digits functions in residue classes. J. Number Theory 79 (1999), 194-216. | MR | Zbl

[17] HOOLEY C.: On the Barban-Davenport-Halberstam theorem III. J. London Math. Soc. 10 (1975), 249-256. | MR | Zbl

[18] KIM D.-H.: On the joint distribution of $q$-additive functions in residue classes. J. Number Theory 74 (1999), 307-336. | MR | Zbl

[19] KIRSCHENHOFER P.-TICHY R.: On the distribution of digits in cantor representations of integers. J. Number Theory 18 (1984), 121-134. | MR | Zbl

[20] LARCHER G.: Bemerkung zur Diskrepanz einer Klasse von Folgen. Anz. Osterreich. Akad. Wiss Math.-Natur. Kl. 1991 (1991), 1-4. | MR | Zbl

[21] MAUDUIT C.-SARKOZY A.: On the arithmetic structure of sets characterized by sum of digits properties. J. Number Theory 61 (1996), 25-38. | MR | Zbl

[22] MAUDUIT C.-SARKOZY A.: On the arithmetic structure of the integers whose sum of digits is fixed. Acta Arith. 81 (1997), 145-173. | MR | Zbl

[23] PARRY W.: On the $\beta$-expansion of real numbers. Acta Math. Acad. Sci. Hung. 11 (1960), 401-416. | MR

[24] PETHÖ A.-TICHY R.: On digit expansions with respect to linear recurrences. J. Number Theory 33 (1989), 243-256. | MR | Zbl

[25] STEINER W.: Digital expansions and the distribution of related functions. Master's thesis, Technical University of Vienna, 2000.

[26] THUSWALDNER J. M.: The sum of digits function in number fields: Distribution in residue classes. J. Number Theory 74 (1999), 111-125. | MR | Zbl