Digital sum moments and substitutions

Jean Marie Dumont; Alain Thomas

Acta Arithmetica (1993)

  • Volume: 64, Issue: 3, page 205-225
  • ISSN: 0065-1036

How to cite

top

Jean Marie Dumont, and Alain Thomas. "Digital sum moments and substitutions." Acta Arithmetica 64.3 (1993): 205-225. <http://eudml.org/doc/206546>.

@article{JeanMarieDumont1993,
author = {Jean Marie Dumont, Alain Thomas},
journal = {Acta Arithmetica},
keywords = {sums of digits; asymptotic behaviour; nowhere differentiable functions; rotation with quadratic angle; moments of the sum-of-digits function; substitution; Parry expansion; integer bases},
language = {eng},
number = {3},
pages = {205-225},
title = {Digital sum moments and substitutions},
url = {http://eudml.org/doc/206546},
volume = {64},
year = {1993},
}

TY - JOUR
AU - Jean Marie Dumont
AU - Alain Thomas
TI - Digital sum moments and substitutions
JO - Acta Arithmetica
PY - 1993
VL - 64
IS - 3
SP - 205
EP - 225
LA - eng
KW - sums of digits; asymptotic behaviour; nowhere differentiable functions; rotation with quadratic angle; moments of the sum-of-digits function; substitution; Parry expansion; integer bases
UR - http://eudml.org/doc/206546
ER -

References

top
  1. [B89] A. Bertrand-Mathis, Comment écrire les nombres entiers dans une base qui n'est pas entière, Acta Math. Hungar. 54 (3-4) (1989), 237-241. Zbl06498007
  2. [C86] J. Coquet, Power sums of digital sums, J. Number Theory 22 (2) (1986), 161-176. Zbl0578.10009
  3. [CV86] J. Coquet and P. van den Bosch, A summation formula involving Fibonacci digits, J. Number Theory 22 (2) (1986), 139-146. Zbl0578.10010
  4. [De75] H. Delange, Sur la fonction sommatoire de la fonction 'somme des chiffres', Enseign. Math. (2) 21 (1) (1975), 31-47. Zbl0306.10005
  5. [D90] J. M. Dumont, Summation formulae for substitutions on a finite alphabet, in: Number Theory and Physics (Les Houches, 1989), Springer Proc. Phys. 47, Springer, Berlin 1990, 185-194. 
  6. [DT89] J. M. Dumont et A. Thomas, Systèmes de numération et fonctions fractales relatifs aux substitutions, Theoret. Comput. Sci. 65 (2) (1989), 153-169. Zbl0679.10010
  7. [DT91] J. M. Dumont et A. Thomas, Digital sum problems and substitutions on a finite alphabet, J. Number Theory 39 (3) (1991), 351-366. Zbl0736.11007
  8. [Fa92] S. Fabre, Substitutions et indépendance des systèmes de numération, thèse, Faculté des sciences de Marseille-Luminy, 1992. 
  9. [FG] P. Flajolet, P. Grabner, P. Kirschenhofer, H. Prodinger and R. Tichy, Mellin transforms and asymptotics: digital sums, Theoret. Comput. Sci., to appear. Zbl0788.44004
  10. [Fr] A. S. Fraenkel, Systems of numeration, Amer. Math. Monthly 92 (2) (1985), 105-114. Zbl0568.10005
  11. [Fro] C. Frougny, Representations of numbers and finite automata, Math. Systems Theory 25 (1) (1992), 37-60. Zbl0776.11005
  12. [GoL87] C. Godrèche, J. M. Luck and F. Vallet, Quasiperiodicity and types of order: a study in one dimension, J. Phys. A 20 (13) (1987), 4483-4499. 
  13. [GTi91] P. Grabner and R. Tichy, α-expansions, linear recurrences, and the sum-of-digits function, Manuscripta Math. 70 (3) (1991), 311-324. Zbl0725.11005
  14. [K90] P. Kirschenhofer, On the variance of the sum-of-digits function, in: Number Theory and Analysis, Lecture Notes in Math. 1452, Springer, Berlin 1990, 112-116. 
  15. [L] J. M. Luck, Private communication. 
  16. [MM] J. L. Mauclaire and L. Murata, An explicit formula for the average of some q-additive functions, in: Prospects of Mathematical Science (Tokyo, 1986), World Sci., Singapore 1988, 141-156. 
  17. [Sh88] J. Shallit, A generalisation of automatic sequences, Theoret. Comput. Sci. 61 (1) (1988), 1-16. 

Citations in EuDML Documents

top
  1. Michael Drmota, Johannes Gajdosik, The distribution of the sum-of-digits function
  2. Mario Lamberger, Jörg M. Thuswaldner, Distribution properties of digital expansions arising from linear recurrences
  3. Jörg M. Thuswaldner, Unimodular Pisot substitutions and their associated tiles
  4. Pierre Arnoux, Valérie Berthé, Arnaud Hilion, Anne Siegel, Fractal representation of the attractive lamination of an automorphism of the free group
  5. Guy Barat, Valérie Berthé, Pierre Liardet, Jörg Thuswaldner, Dynamical directions in numeration

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.