| Title:
|
Distribution properties of digital expansions arising from linear recurrences (English) |
| Author:
|
Lamberger, Mario |
| Author:
|
Thuswaldner, Jörg M. |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
1-20 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11B37 |
| MSC:
|
11K16 |
| MSC:
|
11L07 |
| idZBL:
|
Zbl 1048.11066 |
| idMR:
|
MR1964200 |
| . |
| Date available:
|
2009-09-25T14:11:59Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133265 |
| . |
| Reference:
|
[1] BRAUER A.: On algebraic equations with all but one root in the interior of the unit circle.Math. Nachr. 4 (1951), 250-257. Zbl 0042.01501, MR 0041975 |
| Reference:
|
[2] COQUET J.-RHIN G.-TOFFIN P.: Représentation des entiers naturels et indépendence statistique 2.Ann. Inst. Fourier (Grenoble) 31 (1981), 1-15. MR 0613026 |
| Reference:
|
[3] DELANGE H.: Sur la fonction sommatoire de la fonction "somme des chiffres".Enseign. Math. (2) 21 (1975), 31-47. Zbl 0306.10005, MR 0379414 |
| Reference:
|
[4] DRMOTA M.-GAJDOSIK J.: The distribution of the sum-of-digits function.J. Théor. Nombres Bordeaux 10 (1998), 17-32. Zbl 0916.11049, MR 1827283 |
| Reference:
|
[5] DRMOTA M.-GAJDOSIK J.: The parity of the sum-of-digits-function of generalized zeckendorf representations.Fibonacci Quart 36 (1998), 3-19. Zbl 0926.11006, MR 1605321 |
| Reference:
|
[6] DUMONT J. M.-SIDOROV N.-THOMAS A.: Number of representations related to a linear recurrent basis.Acta Arith. 88 (1999), 371-396. Zbl 0929.11004, MR 1690457 |
| Reference:
|
[7] DUMONT J. M.-THOMAS A.: Digital sum moments and substitutions.Acta Arith. 64 (1993), 205-225. Zbl 0774.11041, MR 1225425 |
| Reference:
|
[8] DUMONT J. M.-THOMAS A.: Gaussian asymptotic properties of the sum-of-digits function.J. Number Theory 62 (1997), 19-38. Zbl 0869.11009, MR 1430000 |
| Reference:
|
[9] FINE N. J.: The distribution of the sum of digits (mod p).Bull. Amer. Math. Soc. 71 (1965), 651-652. Zbl 0148.02005, MR 0184895 |
| Reference:
|
[10] FOUVRY E.-MAUDUIT C.: Sommes des chiffres et nombres presque premiers.Math. Ann. 305 (1996), 571-599. Zbl 0858.11050, MR 1397437 |
| Reference:
|
[11] FROUGNY C.: Representations of numbers and finite automata.Math. Systems Theory 25 (1992), 37-60. Zbl 0776.11005, MR 1139094 |
| Reference:
|
[12] GEL'FOND A. O.: Sur les nombres qui ont des proprietes additives et multiplicatives donnees.Acta Arith. 13 (1968), 259-265. MR 0220693 |
| Reference:
|
[13] GRABNER P.-TICHY R.: Contributions to digit expansions with respect to linear recurrences.J. Number Theory 36 (1990), 160-169. Zbl 0711.11004, MR 1072462 |
| Reference:
|
[14] GRABNER P. J.: Ziffernentwicklungen bezuglich linearer Rekursionen.Anz. Osterreich.Akad. Wiss Math.-Natur. Kl. 1990 (1990), 1-21. MR 1101092 |
| Reference:
|
[15] GRABNER P. J.-TICHY R. F.: \alpha$-expansions, linear recurrences, and the sum-of-digits function.Manuscripta Math. 70 (1991), 311-324. Zbl 0725.11005, MR 1089067 |
| Reference:
|
[16] HOIT A.: The distribution of generalized sum-of-digits functions in residue classes.J. Number Theory 79 (1999), 194-216. Zbl 0999.11043, MR 1728147 |
| Reference:
|
[17] HOOLEY C.: On the Barban-Davenport-Halberstam theorem III.J. London Math. Soc. 10 (1975), 249-256. Zbl 0304.10029, MR 0382204 |
| Reference:
|
[18] KIM D.-H.: On the joint distribution of $q$-additive functions in residue classes.J. Number Theory 74 (1999), 307-336. Zbl 0920.11067, MR 1671677 |
| Reference:
|
[19] KIRSCHENHOFER P.-TICHY R.: On the distribution of digits in cantor representations of integers.J. Number Theory 18 (1984), 121-134. Zbl 0582.10038, MR 0734443 |
| Reference:
|
[20] LARCHER G.: Bemerkung zur Diskrepanz einer Klasse von Folgen.Anz. Osterreich. Akad. Wiss Math.-Natur. Kl. 1991 (1991), 1-4. Zbl 0742.11040, MR 1188720 |
| Reference:
|
[21] MAUDUIT C.-SARKOZY A.: On the arithmetic structure of sets characterized by sum of digits properties.J. Number Theory 61 (1996), 25-38. Zbl 0868.11004, MR 1418316 |
| Reference:
|
[22] MAUDUIT C.-SARKOZY A.: On the arithmetic structure of the integers whose sum of digits is fixed.Acta Arith. 81 (1997), 145-173. Zbl 0887.11008, MR 1456239 |
| Reference:
|
[23] PARRY W.: On the $\beta$-expansion of real numbers.Acta Math. Acad. Sci. Hung. 11 (1960), 401-416. MR 0142719 |
| Reference:
|
[24] PETHÖ A.-TICHY R.: On digit expansions with respect to linear recurrences.J. Number Theory 33 (1989), 243-256. Zbl 0676.10010, MR 1034204 |
| Reference:
|
[25] STEINER W.: Digital expansions and the distribution of related functions.Master's thesis, Technical University of Vienna, 2000. |
| Reference:
|
[26] THUSWALDNER J. M.: The sum of digits function in number fields: Distribution in residue classes.J. Number Theory 74 (1999), 111-125. Zbl 0932.11068, MR 1670564 |
| . |
