Number of representations related to a linear recurrent basis
Jean Marie Dumont; Nikita Sidorov; Alain Thomas
Acta Arithmetica (1999)
- Volume: 88, Issue: 4, page 371-396
- ISSN: 0065-1036
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topJean Marie Dumont, Nikita Sidorov, and Alain Thomas. "Number of representations related to a linear recurrent basis." Acta Arithmetica 88.4 (1999): 371-396. <http://eudml.org/doc/207254>.
@article{JeanMarieDumont1999,
author = {Jean Marie Dumont, Nikita Sidorov, Alain Thomas},
journal = {Acta Arithmetica},
keywords = {number of representations; linear recurrent basis; summation function; Lipschitz exponent; representation graph},
language = {eng},
number = {4},
pages = {371-396},
title = {Number of representations related to a linear recurrent basis},
url = {http://eudml.org/doc/207254},
volume = {88},
year = {1999},
}
TY - JOUR
AU - Jean Marie Dumont
AU - Nikita Sidorov
AU - Alain Thomas
TI - Number of representations related to a linear recurrent basis
JO - Acta Arithmetica
PY - 1999
VL - 88
IS - 4
SP - 371
EP - 396
LA - eng
KW - number of representations; linear recurrent basis; summation function; Lipschitz exponent; representation graph
UR - http://eudml.org/doc/207254
ER -
References
top- [AlZ] J. C. Alexander and D. Zagier, The entropy of a certain infinitely convolved Bernoulli measure, J. London Math. Soc. 44 (1991), 121-134. Zbl0691.58024
- [AllS] J. P. Allouche and J. Shallit, The ring of k-regular sequences, Theoret. Comput. Sci. 98 (1992), 163-197. Zbl0774.68072
- [Be] P. G. Becker, k-regular power series and Mahler-type functional equations, J. Number Theory 49 (1994), 269-286. Zbl0821.11013
- [Bo] D. Bogdanov, Branching graph for the de Rham curve, Master Thesis, St. Petersburg State University, St. Petersburg, 1993.
- [Br] N. G. de Bruijn, On Mahler's partition problem, Indag. Math. 10 (1948), 210-220.
- [Bu] Y. Bugeaud, Sur la suite des nombres de la forme , , to appear. Zbl0061.09302
- [Ca] L. Carlitz, Fibonacci representations, Fibonacci Quart. 6 (1968), 193-220. Zbl0167.03901
- [Co] A. Cobham, Uniform tag sequences, Math. Systems Theory 6 (1972), 164-192. Zbl0253.02029
- [D] P. Dumas, Récurrences Mahlériennes, suites automatiques, et études asymptotiques, Doctorat de mathématiques, Université de Bordeaux, 1993.
- [DF] P. Dumas et P. Flajolet, Asymptotique des récurrences mahlériennes: le cas cyclotomique, J. Théor. Nombres Bordeaux 8 (1996), 1-30.
- [DuT] J. M. Dumont et A. Thomas, Systèmes de numération et fonctions fractales relatifs aux substitutions, Theoret. Comput. Sci. 65 (1989), 153-169. Zbl0679.10010
- [E] P. Erdős, On a family of symmetric Bernoulli convolutions, Amer. J. Math. 61 (1939), 974-976. Zbl0022.35402
- [Fr] C. Frougny, Representations of numbers and finite automata, Math. Systems Theory 25 (1992), 37-60. Zbl0776.11005
- [JW] B. Jessen and A. Wintner, Distribution functions and the Riemann zeta function, Trans. Amer. Math. Soc. 38 (1938), 48-88. Zbl0014.15401
- [KP] B. Kovács and A. Pethő, Number systems in integral domains, especially in orders of algebraic number fields, Acta Sci. Math. (Szeged) 55 (1991), 287-299. Zbl0760.11002
- [LaNg] K.-S. Lau and S.-M. Ngai, -spectrum of the Bernoulli convolution associated with the golden ratio, Studia Math. 131 (1998), 225-251. Zbl0929.28005
- [Po] A. J. van der Poorten, An introduction to continued fractions, in: Diophantine Analysis, London Math. Soc. Lecture Note Ser. 109, Cambridge Univ. Press, 1986, 99-138.
- [Pu] I. Pushkarev, The ideal lattices of multizigzags and the enumeration of Fibonacci partitions, Zap. Nauchn. Sem. POMI 223 (1995), 280-312 (in Russian). Zbl0909.05003
- [Rh] G. de Rham, Sur une courbe plane, J. Math. Pures Appl. 35 (1956), 25-42. Zbl0070.39101
- [Ru] W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, New York, 1964.
- [S] N. A. Sidorov, The summation function for the number of Fibonacci representations, PDMI preprint 15/1995, 1-17.
- [SV] N. A. Sidorov and A. M. Vershik, Ergodic properties of the Erdős measure, the entropy of the goldenshift, and related problems, Monatsh. Math. 126 (1998), 215-261. Zbl0916.28012
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