Indépendance algébrique et exponentielle de Carlitz

Laurent Denis

Acta Arithmetica (1995)

  • Volume: 69, Issue: 1, page 75-89
  • ISSN: 0065-1036

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Laurent Denis. "Indépendance algébrique et exponentielle de Carlitz." Acta Arithmetica 69.1 (1995): 75-89. <http://eudml.org/doc/206673>.

@article{LaurentDenis1995,
author = {Laurent Denis},
journal = {Acta Arithmetica},
keywords = {derivatives of the Carlitz exponential; transcendence; transcendency degree},
language = {fre},
number = {1},
pages = {75-89},
title = {Indépendance algébrique et exponentielle de Carlitz},
url = {http://eudml.org/doc/206673},
volume = {69},
year = {1995},
}

TY - JOUR
AU - Laurent Denis
TI - Indépendance algébrique et exponentielle de Carlitz
JO - Acta Arithmetica
PY - 1995
VL - 69
IS - 1
SP - 75
EP - 89
LA - fre
KW - derivatives of the Carlitz exponential; transcendence; transcendency degree
UR - http://eudml.org/doc/206673
ER -

References

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  1. [A] G. Anderson, t-motives, Duke Math. J. 53 (1986), 457-502. 
  2. [A-T] G. Anderson and D. Thakur, Tensor powers of the Carlitz module and zeta values, Ann. of Math. 132 (1990), 159-191. Zbl0713.11082
  3. [B-B-T] P.-G. Becker, W. D. Brownawell and R. Tubbs, Gelfond's theorem for Drinfeld modules, Michigan Math. J. 41 (1994), 219-233, and Abstracts Amer. Math. Soc. 82 (1992), 359. 
  4. [C] L. Carlitz, On certain functions connected with polynomials in a Galois field, Duke Math. J. 1 (1935), 137-168. Zbl0012.04904
  5. [D1] L. Denis, Théorème de Baker et modules de Drinfeld, J. Number Theory 43 (1993), 203-215. Zbl0767.11029
  6. [D2] L. Denis, Remarques sur la transcendance en caractéristique finie, C. R. Acad. Sci. Canada 14 (1992), 157-162. 
  7. [D3] L. Denis, Transcendance et dérivées de l'exponentielle de Carlitz, dans: Séminaire de Théorie des Nombres de Paris, Birkhäuser, 1993, 1-21. 
  8. [D4] L. Denis, Dérivées d'un module de Drinfeld et transcendance, soumis pour publication. 
  9. [D5] L. Denis, Indépendance algébrique sur le module de Carlitz, C. R. Acad. Sci. Paris Sér. I 317 (1993), 913-915. 
  10. [L] S. Lang, Algebra, 3rd ed., Addison-Wesley, 1993. 
  11. [T1] A. Thiery, Indépendance algébrique de périodes et quasi-périodes de modules de Drinfeld, dans: The Arithmetic of Function Fields, Proceedings of the Workshop at Ohio State University, D. Goss, D. Hayes, M. Rosen (eds.), Walter de Gruyter, 1992, 265-284. 
  12. [T2] A. Thiery, Théorème de Lindemann-Weierstrass pour les modules de Drinfeld, Thèse de l'Université de Caen, et preprint, 1992. 
  13. [W] L. Wade, Transcendence properties of the Carlitz Ψ function, Duke Math. J. 13 (1946), 79-85. Zbl0063.08107
  14. [Wa] M. Waldschmidt, Nombres transcendants, Lecture Notes in Math. 402, Springer, 1974. Zbl0302.10030
  15. [Y1] J. Yu, Transcendence theory over function fields, Duke Math. J. 52 (1985), 517-527. Zbl0574.12015
  16. [Y2] J. Yu, Transcendence and Drinfeld modules: Several variables, ibid. 58 (1989), 559-575. Zbl0687.12008
  17. [Y3] J. Yu, Transcendence and special zeta values in characteristic p, Ann. of Math. 134 (1991), 1-23. Zbl0734.11040
  18. [Y4] J. Yu, Analytic homomorphisms into Drinfeld modules, preprint, 1991. 
  19. [Y5] J. Yu, A six exponentials theorem in finite characteristic, Math. Ann. 272 (1985), 91-98. Zbl0574.12014
  20. [Z-S] O. Zariski and P. Samuel, Commutative Algebra, Vol. 1, Springer, 1979. 

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