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no. 1
Subword complexity and finite characteristic numbers
Alina Firicel1
1 Université de Lyon Université Lyon 1 Institut Camille Jordan UMR 5208 du CNRS 43, boulevard du 11 novembre 1918 F-69622 Villeurbanne Cedex, France
Actes des rencontres du CIRM, Volume 1 (2009) no. 1, pp. 29-34.
  • Abstract

Decimal expansions of classical constants such as 2, π and ζ(3) have long been a source of difficult questions. In the case of finite characteristic numbers (Laurent series with coefficients in a finite field), where no carry-over difficulties appear, the situation seems to be simplified and drastically different. On the other hand, the theory of Drinfeld modules provides analogs of real numbers such as π, e or ζ values. Hence, it became reasonable to enquire how “complex” the Laurent representation of these “numbers” is.

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Published online: 2010-08-30
Zbl: 06938554
DOI: 10.5802/acirm.6
Author's affiliations:
Alina Firicel 1

1 Université de Lyon Université Lyon 1 Institut Camille Jordan UMR 5208 du CNRS 43, boulevard du 11 novembre 1918 F-69622 Villeurbanne Cedex, France
  • BibTeX
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@article{ACIRM_2009__1_1_29_0,
     author = {Alina Firicel},
     title = {Subword complexity and finite characteristic numbers},
     journal = {Actes des rencontres du CIRM},
     pages = {29--34},
     publisher = {CIRM},
     volume = {1},
     number = {1},
     year = {2009},
     doi = {10.5802/acirm.6},
     zbl = {06938554},
     language = {en},
     url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.6/}
}
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PB  - CIRM
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Alina Firicel. Subword complexity and finite characteristic numbers. Actes des rencontres du CIRM, Volume 1 (2009) no. 1, pp. 29-34. doi : 10.5802/acirm.6. https://acirm.centre-mersenne.org/articles/10.5802/acirm.6/
  • References
  • Cited by

[1] B. Adamczewski & Y. Bugeaud, On the complexity of algebraic numbers I. Expansions in integer bases, Annals of Mathematics 165 (2007), 547–565. | DOI | MR | Zbl

[2] B. Adamczewski & Y. Bugeaud & F. Luca, Sur la complexité des nombres algébriques. C. R. Math. Acad. Sci. Paris, 339(2004), 11-14. | DOI | Zbl

[3] J.-P. Allouche, Sur la transcendance de la série formelle Π, Journal de Théorie des Nombres de Bordeaux 2 (1990), 103–117. | DOI | Zbl

[4] J.-P. Allouche & J. Shallit, Automatic Sequences: Theory, Applications, Generalizations, Cambridge University Press, Cambridge, 2003. | DOI

[5] David H. Bailey, Peter B. Borwein and Simon Plouffe, On the Rapid Computation of Various Polylogarithmic Constants, Mathematics of Computation, vol. 66, no. 218 (1997), pg. 903?-913. | DOI | MR | Zbl

[6] R.M. Beals & D.S. Thakur, Computational classification of numbers and algebraic properties, Internat. Math. Res. Notices, 15 (1998), 799–818. | DOI | Zbl

[7] J. Berstel and P. Séébold , Algebraic combinatorics on Words, chapter Sturmian words, Cambridge University Press (2002).

[8] V. Berthé, Automates et valeurs de transcendance du logarithme de Carlitz Acta Arithmetica LXVI.4 (1994), 369–390. | DOI | MR | Zbl

[9] V. Berthé, Combinaisons linéaires de ζ(s)/Π s sur F q (x), pour 1≤s≤q-2 J. Number Theory 53 (1995), 272–299. | DOI | Zbl

[10] V. Berthé, De nouvelles preuves preuves “automatiques” de transcendance pour la fonction zeta de Carlitz Journées Arithmétiques de Genève, Astérisque 209 (1992), 159–168 . | Zbl

[11] V. Berthé, Fonction zeta de Carlitz et automates, Journal de Théorie des Nombres de Bordeaux 5 (1993), 53–77. | DOI | MR | Zbl

[12] L. Carlitz, On certain functions connected with polynomials in a Galois field, Duke Math. J., 1 (1935), 137–168. | DOI | MR | Zbl

[13] D. G. Champernowne, The construction of decimals normal in the scale of ten, J. London Math. Soc. (1933), 8, 254?-260. | DOI | MR | Zbl

[14] H. Cherif, B. de Mathan, Irrationality measures of Carlitz zeta values in characteristic p, J. Number Theory 44 (1993), 260–272. | DOI | MR | Zbl

[15] Christol, G.; Kamae, T.; Mendès France, Michel; Rauzy, Gérard, Suites algébriques, automates et substitutions, Bulletin de la Société Mathématique de France, 108 (1980), 401–419. | DOI | Zbl

[16] A. Cobham, Uniform tag sequences, Math. Systems Theory 6 (1972), 164–192. | DOI | MR | Zbl

[17] A. Firicel, Subword Complexity and Laurent series over finite fields, in progress.

[18] D. Goss, Basic Structures of Function Field Arithmetic, Springer-Verlag, Berlin, 1996. | DOI | Zbl

[19] M. Morse & G. A. Hedlund, Symbolic dynamics, Amer. J. Math. 60 (1938), 815–866. | DOI | MR | Zbl

[20] D.S. Thakur, Function Field Arithmetic, World Scientfic, Singapore, 2004. | DOI | Zbl

[21] L.J. Wade, Certain quantities transcendental over GF(p n )(x), Duke Math. J. 8 (1941), 701–720. | DOI | Zbl

[22] J. Yu, Transcendence and Special Zeta Values in Characteristic p, Annals of Math. 134 (1991), 1–23. | DOI | MR | Zbl

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