Fonctions zêta en caractéristique positive et modules de Carlitz-Hayes

 Access to full text

 Full (PDF)

1. [1] E. Artin - Quadratische Kôrper im Gebiete der höheren Kongruenzen I, II, Math. Z19 (1924) 153-246 (oeuvres1-94). Zbl50.0107.01MR1544651JFM50.0107.01
2. [2] J.-P. Allouche - Sur la transcendance de la série formelle II, in Séminaire de Théorie des Nombres de Bordeaux1990, 103-117. Zbl0709.11067MR1061761
3. [3] J.-P. Allouche - Fonction zêta de Carlitz et automates finis, in Modules de Drinfeld et Approximation Diophantienne (éd. Y. Hellegouarch)Caen, 1990. 
4. [4] V. Berthé - Automates et valeurs de transcendance du logarithme de Carlitz, Acta Arith.LXVI4 (1994), 369-390. Zbl0784.11024MR1288353
5. [5] V. Berthé - Combinaisons linéaires de ζ(s)/Πs sur Fq (x), pour 1 ≤ s ≤ q - 2, J. Number Theory53 (1995), 272-299. Zbl0853.11062
6. [6] N. Bourbaki - Algèbre, ch. 5, Hermann, 1959. 
7. [7] L. Carlitz - On certain functions connected with polynomials in a Galois field, Duke Math. J.1 (1935), 137-168. Zbl0012.04904JFM61.0127.01
8. [8] L. Carlitz - A class ofpolynomials, Trans. Amer. Math. Soc. (1938), 167-182. JFM64.0093.01
9. [9] L. Carlitz - An analogue of the von Staudt-Clausen theorem, Duke Math. J.3 (1937), 503-517. Zbl63.0879.03JFM63.0879.03
10. [10] L. Carlitz - An analogue of the von Staudt-Clausen theorem, Duke Math. J.7 (1940), 62-67. Zbl0024.24410JFM66.0056.01
11. [11] H. Cherif, B. de Mathan - Irrationality measures of Carlitz zeta values in characteristic p, J. Number Theory44 (1993), 260-272. Zbl0780.11031
12. [12] G. Christol, T. Kamae, M. Mendès-France, G. Rauzy - Suites al- gébriques, automates et substitutions, Bull. Soc. Math. France108 (1980), 401-419. Zbl0472.10035
13. [13] P.M. Cohn - Skew Field Constructions, L.M.S. Lect. Notes, 1977, Cambridge. Zbl0355.16009
14. [14] G. Damamme, Y. Hellegouarch - Transcendence of the values of the Carlitz zeta function by Wade's method, J. Number Theory39 (1991), 257-278. Zbl0743.11070
15. [15] P. Deligne, D. Husemöller - Survey of Drinfeld modules, Contemp. Math.67 (1987), 25-91. Zbl0627.14026
16. [16] L. Denis - Un critère de transcendance en caractéristique finie, Journ. of Algebra182, 2, (1996), 522-533. Zbl0857.11029
17. [17] V.G. Drinfeld - Elliptic modules, Math. USSR Sbornik23 (1976), 561-592. Zbl0321.14014
18. [18] V.G. Drinfeld - Elliptic modules II, Math. USSR Sbornik31 (1977), 159-170. Zbl0386.20022
19. [19] D. Dummit - Genus two hyperelliptic Drinfeld modules over F2 , in The Arithmetic of Function Fields (éds D. Goss et al) (1992), 117-129. Zbl0793.11016
20. [20] D. Dummit, D. Hayes - Rank-one Drinfeld modules of elliptic curves, Math. Comp.62 (1994), 875-883. Zbl0793.11017
21. [21] J. Fresnel, M. Koskas, B. de Mathan - Automata and transcendance in positive characteristics, Prépub. Univ. Bordeaux (1997). 
22. [22] S. Galovich, M. Rosen - Units and class groups in cyclotomic function fields, J. Number Theory14 (1982), 156-184. Zbl0483.12003
23. [23] E.V. Gekeler - On regularity of small primes in functions fields, J. Number Theory34 (1990), 114-127. Zbl0695.12008
24. [24] E.V. Gekeler - On finite Drinfeld Modules, J. Algebra141 (1991), 187-203. Zbl0731.11034
25. [25] D. Goss - L-series of t—motives and Drinfeld modules, in The Arithmetic of Function Fields (éds D. Goss et al) de Gruyter (1992), 313-402. Zbl0806.11028
26. [26] D. Goss - Basic Structures of Function Field Arithmetic, Springer (1996). Zbl0892.11021
27. [27] D. Goss - Separability, Multi-valued operators and zeros of L-functions, Prépub. (1997). 
28. [28] D. Hayes - Explicit class field theory for rational function fields, Trans. Amer. Math. Soc.189 (1974), 77-91. Zbl0292.12018
29. [29] D. Hayes - A brief introduction to Drinfeld modules, in The Arithmetic of Function Fields (éds D. Goss et al) de Gruyter (1992), 1-32. Zbl0793.11015
30. [30] Y. Hellegouarch - Galois calculus and Carlitz exponentials, in The Arithmetic of Function Fields (éds D. Goss et al), de Gruyter (1992), 33-50. Zbl0794.11025
31. [31] Y. Hellegouarch - Une généralisation d'un critère de de Mathan, C.R. Acad. Sci. Paris, t. 321, I (1995), 677-680. Zbl0844.11049
32. [32] B. de Mathan - Irrationality measures and transcendance in positive charac- teristic, J. Number Theory54 (1995), 93-112. Zbl0832.11022
33. [33] V. Mauduit - Explicit reciprocity law for a rank one Drinfeld Fq [t]-module, in Drinfeld Modules, Modular Schemes and Applications (éds E.-U. Gekeler et al), World Scientific (1997), 282-297. Zbl0924.11049
34. [34] O. Ore - On a Special class of polynomials, Trans. Amer. Math. Soc.35 (1933), 559-584. Zbl0007.15102
35. [35] O. Ore - Theory of non-commutative polynomials, Annals of Math.34 (1933), 480-508. Zbl0007.15101JFM59.0925.01
36. [36] F. Recher - Propriétés de transcendance de séries formelles provenant de l'exponentielle de Carlitz, C.R. Acad. Sc. Paris, Série I, t. 315 (1992), 245- 250. Zbl0757.11017
37. [37] M. Rosen - The Hilbert class field in function fields, Expos. Math.5 (1987), 365-378. Zbl0632.12017
38. [38] F.B. Schultheis - Carlitz-Kummer function fields, J. Number Theory36 (1990), 133-144. Zbl0712.11067
39. [39] F.B. Schultheis - Explicit reciprocity laws in algebraic function fields, Thesis, UMT Ann Arbor, (1987). 
40. [40] J.-P. Serre - Zeta and L-functions, in Arithmetic Algebraic Geometry, Proc. of a conference held at Purdue Univ. Harper and Row, New York (1965), 82-92. Zbl0171.19602
41. [41] J.-P. Serre - Complex multiplication, in Algebraic Number Theory, J.W.S. Cassels and A. Fröhlich éds, Ac. Press, London, 1967. 
42. [42] T. Takahashi - Good reduction of elliptic modules, J. Math. Soc. of Japan34 (1982), 475-487. Zbl0476.14010
43. [43] J. Tate - Number theoretic background, in Proceedings Symposia in Pure Mathematics33, Part 2, Amer. Math. Soc. (1979), 3-26. Zbl0422.12007
44. [44] D. Thakur - On characteristic p zeta functions, Compositio Math.99 (1995), 231-247. Zbl0841.11030
45. [45] A. Thiery - Indépendance algébrique des périodes et quasi-périodes d'un module de Drinfeld, in The Arithmetic of Function Fields (éds Goss et al) (1992), 265-284. Zbl0798.11021
46. [46] L. Wade - Certain quantities transcendent over GF(pn,x) I, Duke Math. J.8 (1941), 707-729. Zbl0063.08101
47. [47] L. Wade - Certain quantities transcendent over GF(pn,x) II, Duke Math. J.10 (1943), 587-594. Zbl0063.08102
48. [48] M. Waldschmidt - Transcendence problems connected with Drinfeld modules, Istambul Üniv. Fen. Fak. Mat. Du.49 (1990), 57-75. Zbl0802.11023
49. [49] D. Wan - On the Riemann hypothesis for the characteristic p zeta function, J. Number Theory58 (1996), 196-212. Zbl0858.11030
50. [50] A. Weil - Basic Number Theory, Die Grundlehren der Mathematischen Wissenschaften144, Springer (1967). Zbl0176.33601
51. [51] J. Yu - Transcendence and special zeta-values in characteristic p, Ann. of Maths134 (1991), 1-23. Zbl0734.11040
52. [52] J. Yu - Transcendence in finite characteristics, in The Arithmetic of Function Fields (éds. D. Goss et al) de Gruyter (1992), 253-264. Zbl0792.11015