The distribution of the sum-of-digits function

Journal de Theorie des Nombres de Bordeaux

Volumn 10, Issue 1, 1998, Pages 17-32

  Drmota, Michael ^a   Gajdosik, Johannes ^a  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85009921485     PISSN: 12467405     EISSN: None     Source Type: Journal    
DOI: 10.5802/jtnb.216     Document Type: Article

References (20)

1. N. L. Bassily and I. Kátai, Distribution of the values of q-additive functions on polynomial sequences, Acta Math. Hung. 68 (1995), 353-361.
2. R. Bellman and H. N. Shapiro, On a problem in additive number theory, Ann. Math. 49 (1948), 333-340.
3. L. E. Bush, An asymptotic formula for the average sum of the digits of integers, Am. Math. Monthly 47 (1940), 154-156.
4. J. Coquet, Power sums of digital sums, J. Number Th. 22 (1986), 161-176.
5. H. Delange Sur la fonction sommatoire de la fonction "Somme de Chiffres", L’Enseignement math. 21 (1975), 31-77.
6. M. Drmota and M. Skalba, The parity of the Zeckendorf sum-of-digits-function, preprint.
7. J. M. Dumont and A. Thomas, Digital sum moments and substitutions, Acta Arith. 64 (1993), 205-225.
8. J. M. Dumont and A. Thomas, Gaussian asymptotic properties of the sum-of-digits functions, J. Number Th. 62 (1997), 19-38.
9. C.-G. Esseen, Fourier analysis of distribution functions. A mathematical study of the Laplace-Gaussian law, Acta Math. 77 (1945), 1-125.
10. J. Gajdosik, Kombinatorische Faktorisierungen und Ziffernentwicklungen, thesis, TU Wien, 1996.
11. P. J. Grabner, P. Kirschenhofer, H. Prodinger, and R. F. Tichy, On the moments of the sum-of-digits function, in: Applications of Fibonacci Numbers 5 (1993), 263-271
12. P. J. Grabner and R. F. Tichy, Contributions to digit expansions with respect to linear recurrences, J. Number Th. 36 (1990), 160-169.
13. P. Grabner and R. F. Tichy, α-Expansions, linear recurrences, and the sum-of-digits function, manuscripta math. 70 (1991), 311-324.
14. R. E. Kennedy and C. N. Cooper, An extension of a theorem by Cheo and Yien concerning digital sums, Fibonacci Q. 29 (1991), 145-149.
15. P. Kirschenhofer, On the variance of the sum of digits function, Lecture Notes Math. 1452 (1990), 112-116.
16. W. Parry, On the,β-expansion of real numbers, Acta Math. Acad. Sci. Hung., 12 (1961), 401-416.
17. A. Pethö and R. F. Tichy, On digit expansions with respect to linear recurrences, J. Number Th. 33 (1989), 243-256.
18. J. Schmid, The joint distribution of the binary digits of integer multiples, Acta Arith. 43 (1984), 391-415.
19. W. M. Schmidt, The joint distribution the digits of certain integer s-tuples, Studies in pure mathematics, Mem. of P. Turan (1983), 605-622.
20. H. Trollope, An explicit expression for binary digital sums, Meth. Mag. 41 (1968), 21-25.