regular language; additive function; numeration system
Abstract :
[en] Asymptotic formulae for the summatory function of additive arithmetic functions related to numeration systems given by regular languages are derived.
Disciplines :
Mathematics
Author, co-author :
Grabner, Peter J.
Rigo, Michel ; Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Additive functions with respect to numeration systems on regular languages
Publication date :
July 2003
Journal title :
Monatshefte für Mathematik
ISSN :
0026-9255
eISSN :
1436-5081
Publisher :
Springer-Verlag Wien, Vienna, Austria
Volume :
139
Issue :
3
Pages :
205-219
Peer reviewed :
Peer Reviewed verified by ORBi
Commentary :
The original publication is available at www.springerlink.com
Barat G, Downarowicz T, Iwanik A, Liardet P (2000) Propriétés topologiques et combinatoires des échelles de numération. Colloq Math 84/85: 285-306
Barat G, Grabner PJ (1996) Distribution properties of G-additive functions. J Number Theory 60: 103-123
Bruyère V, Hansel G (1997) Bertrand numeration systems and recognizability. Theor Comput Sci 181: 17-43, Latin American Theoretical Informatics (Valparaiso, 1995)
Delange H (1972) Sur les fonctions q-additive ou q-multiplicatives. Acta Arith 21: 285-298
Delange H (1975) Sur la fonction sommatoire de la fonction "Somme des Chiffres". Enseign Math II Sér 21: 31-47
Drmota M (1997) q-Additive functions and well distribution. Demonstr Math 30: 883-896
Drmota M, Gajdosik J (1998) The distribution of the sum-of-digits function. J Théor Nombres Bordeaux 10: 17-32
Dumont J-M, Thomas A (1991) Digital sum problems and substitutions on a finite alphabet. J Number Theory 39: 351-366
Dumont J-M, Thomas A (1993) Digital sum moments and substitutions. Acta Arith 64: 205-225
Dumont J-M, Thomas A (1997) Gaussian asymptotic properties of the sum-of-digits function. J Number Theory 62: 19-38
Eilenberg S (1974) Automata, Languages and Machines, vol. A. New York: Academic Press
Frougny C (1992) Representation of numbers and finite automata. Math Syst Theory 25: 37-60
Frougny C (2002) Numeration Systems. In: Lothaire M (ed) Algebraic Combinatorics on Words. Encyclopedia of Mathematics and its Applications, vol. 90. Cambridge: Univ Press
Grabner PJ, Liardet P, Tichy RF (1995) Odometers and systems of numeration. Acta Arith 70: 103-123
Grabner PJ, Tichy RF (1990) Contributions to digit expansions with respect to linear recurrences. J Number Theory 36: 160-169
Grabner PJ, Tichy RF (1991) α-expansions, linear recurrences and the sum-of-digits function. Manuscr Math 70: 311-324
Lecomte P, Rigo M (2001) Numeration systems on a regular language. Theory Comput Syst 34: 27-44
Lecomte P, Rigo M (2002) On the representation of real numbers using regular languages. Theory Comput Syst 35: 13-38
Loraud N (1995) β-shift, systèmes de numération et automates. J Théor Nombres Bordeaux 7: 473-498
Shallit JO (1994) Numeration systems, linear recurrences, and regular sets. Inform and Comput 113: 331-347
Szilard A, Yu S, Zhang K, Shallit J (1992) Characterizing regular languages with polynomial densities. In: Mathematical Foundations of Computer Science 1992 (Prague, 1992). Lect Notes Comput Sci 629: 494-503. Berlin: Springer
Zeckendorf E (1972) A generalized Fibonacci numeration. Fibonacci Quart 10: 365-372
