Distribution properties of digital expansions arising from linear recurrences

Mario Lamberger; Jörg M. Thuswaldner

Mathematica Slovaca (2003)

  • Volume: 53, Issue: 1, page 1-20
  • ISSN: 0139-9918

How to cite

top

Lamberger, Mario, and Thuswaldner, Jörg M.. "Distribution properties of digital expansions arising from linear recurrences." Mathematica Slovaca 53.1 (2003): 1-20. <http://eudml.org/doc/32421>.

@article{Lamberger2003,
author = {Lamberger, Mario, Thuswaldner, Jörg M.},
journal = {Mathematica Slovaca},
keywords = {linear recurrences; number systems; exponential sum estimates},
language = {eng},
number = {1},
pages = {1-20},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Distribution properties of digital expansions arising from linear recurrences},
url = {http://eudml.org/doc/32421},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Lamberger, Mario
AU - Thuswaldner, Jörg M.
TI - Distribution properties of digital expansions arising from linear recurrences
JO - Mathematica Slovaca
PY - 2003
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 53
IS - 1
SP - 1
EP - 20
LA - eng
KW - linear recurrences; number systems; exponential sum estimates
UR - http://eudml.org/doc/32421
ER -

References

top
  1. BRAUER A., On algebraic equations with all but one root in the interior of the unit circle, Math. Nachr. 4 (1951), 250-257. (1951) Zbl0042.01501MR0041975
  2. COQUET J.-RHIN G.-TOFFIN P., Représentation des entiers naturels et indépendence statistique 2, Ann. Inst. Fourier (Grenoble) 31 (1981), 1-15. (1981) MR0613026
  3. DELANGE H., Sur la fonction sommatoire de la fonction "somme des chiffres", Enseign. Math. (2) 21 (1975), 31-47. (1975) Zbl0306.10005MR0379414
  4. DRMOTA M.-GAJDOSIK J., The distribution of the sum-of-digits function, J. Théor. Nombres Bordeaux 10 (1998), 17-32. (1998) Zbl0916.11049MR1827283
  5. DRMOTA M.-GAJDOSIK J., The parity of the sum-of-digits-function of generalized zeckendorf representations, Fibonacci Quart 36 (1998), 3-19. (1998) Zbl0926.11006MR1605321
  6. DUMONT J. M.-SIDOROV N.-THOMAS A., Number of representations related to a linear recurrent basis, Acta Arith. 88 (1999), 371-396. (1999) Zbl0929.11004MR1690457
  7. DUMONT J. M.-THOMAS A., Digital sum moments and substitutions, Acta Arith. 64 (1993), 205-225. (1993) Zbl0774.11041MR1225425
  8. DUMONT J. M.-THOMAS A., Gaussian asymptotic properties of the sum-of-digits function, J. Number Theory 62 (1997), 19-38. (1997) Zbl0869.11009MR1430000
  9. FINE N. J., The distribution of the sum of digits (mod p), Bull. Amer. Math. Soc. 71 (1965), 651-652. (1965) Zbl0148.02005MR0184895
  10. FOUVRY E.-MAUDUIT C., Sommes des chiffres et nombres presque premiers, Math. Ann. 305 (1996), 571-599. (1996) Zbl0858.11050MR1397437
  11. FROUGNY C., Representations of numbers and finite automata, Math. Systems Theory 25 (1992), 37-60. (1992) Zbl0776.11005MR1139094
  12. GEL'FOND A. O., Sur les nombres qui ont des proprietes additives et multiplicatives donnees, Acta Arith. 13 (1968), 259-265. (1968) MR0220693
  13. GRABNER P.-TICHY R., Contributions to digit expansions with respect to linear recurrences, J. Number Theory 36 (1990), 160-169. (1990) Zbl0711.11004MR1072462
  14. GRABNER P. J., Ziffernentwicklungen bezuglich linearer Rekursionen, Anz. Osterreich.Akad. Wiss Math.-Natur. Kl. 1990 (1990), 1-21. (1990) MR1101092
  15. GRABNER P. J.-TICHY R. F., [unknown], Manuscripta Math. 70 (1991), 311-324. (1991) Zbl0725.11005MR1089067
  16. HOIT A., The distribution of generalized sum-of-digits functions in residue classes, J. Number Theory 79 (1999), 194-216. (1999) Zbl0999.11043MR1728147
  17. HOOLEY C., On the Barban-Davenport-Halberstam theorem III, J. London Math. Soc. 10 (1975), 249-256. (1975) Zbl0304.10029MR0382204
  18. KIM D.-H., On the joint distribution of q -additive functions in residue classes, J. Number Theory 74 (1999), 307-336. (1999) Zbl0920.11067MR1671677
  19. KIRSCHENHOFER P.-TICHY R., On the distribution of digits in cantor representations of integers, J. Number Theory 18 (1984), 121-134. (1984) Zbl0582.10038MR0734443
  20. LARCHER G., Bemerkung zur Diskrepanz einer Klasse von Folgen, Anz. Osterreich. Akad. Wiss Math.-Natur. Kl. 1991 (1991), 1-4. (1991) Zbl0742.11040MR1188720
  21. MAUDUIT C.-SARKOZY A., On the arithmetic structure of sets characterized by sum of digits properties, J. Number Theory 61 (1996), 25-38. (1996) Zbl0868.11004MR1418316
  22. MAUDUIT C.-SARKOZY A., On the arithmetic structure of the integers whose sum of digits is fixed, Acta Arith. 81 (1997), 145-173. (1997) Zbl0887.11008MR1456239
  23. PARRY W., On the β -expansion of real numbers, Acta Math. Acad. Sci. Hung. 11 (1960), 401-416. (1960) MR0142719
  24. PETHÖ A.-TICHY R., On digit expansions with respect to linear recurrences, J. Number Theory 33 (1989), 243-256. (1989) Zbl0676.10010MR1034204
  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. (1999) Zbl0932.11068MR1670564

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.