Indépendance algébrique et exponentielle de Carlitz

Laurent Denis

Acta Arithmetica (1995)

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

How to cite


Laurent Denis. "Indépendance algébrique et exponentielle de Carlitz." Acta Arithmetica 69.1 (1995): 75-89. <>.

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 = {},
volume = {69},
year = {1995},

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 -
ER -


  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. 

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.