Fonctions zêta en caractéristique positive et modules de Carlitz-Hayes
Séminaire Bourbaki : volume 1997/98, exposés 835-849, Astérisque, no. 252 (1998), Talk no. 837, 23 p.
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Hellegouarch, Yves. Fonctions zêta en caractéristique positive et modules de Carlitz-Hayes, in Séminaire Bourbaki : volume 1997/98, exposés 835-849, Astérisque, no. 252 (1998), Talk no. 837, 23 p. http://archive.numdam.org/item/SB_1997-1998__40__57_0/

[1] E. Artin - Quadratische Kôrper im Gebiete der höheren Kongruenzen I, II, Math. Z 19 (1924) 153-246 (oeuvres 1-94). | DOI | JFM | MR

[2] J.-P. Allouche - Sur la transcendance de la série formelle II, in Séminaire de Théorie des Nombres de Bordeaux 1990, 103-117. | DOI | EuDML | Numdam | MR | Zbl

[3] J.-P. Allouche - Fonction zêta de Carlitz et automates finis, in Modules de Drinfeld et Approximation Diophantienne (éd. Y. Hellegouarch) Caen, 1990.

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

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

[6] N. Bourbaki - Algèbre, ch. 5, Hermann, 1959. | Zbl

[7] L. Carlitz - On certain functions connected with polynomials in a Galois field, Duke Math. J. 1 (1935), 137-168. | DOI | JFM

[8] L. Carlitz - A class ofpolynomials, Trans. Amer. Math. Soc. (1938), 167-182. | DOI | JFM

[9] L. Carlitz - An analogue of the von Staudt-Clausen theorem, Duke Math. J. 3 (1937), 503-517. | DOI | JFM

[10] L. Carlitz - An analogue of the von Staudt-Clausen theorem, Duke Math. J. 7 (1940), 62-67. | DOI | JFM

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

[12] G. Christol, T. Kamae, M. Mendès-France, G. Rauzy - Suites algébriques, automates et substitutions, Bull. Soc. Math. France 108 (1980), 401-419. | DOI | EuDML | Numdam | Zbl

[13] P. M. Cohn - Skew Field Constructions, L.M.S. Lect. Notes, 1977, Cambridge. | Zbl

[14] G. Damamme, Y. Hellegouarch - Transcendence of the values of the Carlitz zeta function by Wade's method, J. Number Theory 39 (1991), 257-278. | DOI | Zbl

[15] P. Deligne, D. Husemöller - Survey of Drinfeld modules, Contemp. Math. 67 (1987), 25-91. | DOI | Zbl

[16] L. Denis - Un critère de transcendance en caractéristique finie, Journ. of Algebra 182, 2, (1996), 522-533. | DOI | Zbl

[17] V. G. Drinfeld - Elliptic modules, Math. USSR Sbornik 23 (1976), 561-592. | DOI | Zbl

[18] V. G. Drinfeld - Elliptic modules II, Math. USSR Sbornik 31 (1977), 159-170. | DOI | Zbl

[19] D. Dummit - Genus two hyperelliptic Drinfeld modules over F2 , in The Arithmetic of Function Fields (éds D. Goss et al) (1992), 117-129. | Zbl

[20] D. Dummit, D. Hayes - Rank-one Drinfeld modules of elliptic curves, Math. Comp. 62 (1994), 875-883. | Zbl

[21] J. Fresnel, M. Koskas, B. De Mathan - Automata and transcendance in positive characteristics, Prépub. Univ. Bordeaux (1997). | Zbl

[22] S. Galovich, M. Rosen - Units and class groups in cyclotomic function fields, J. Number Theory 14 (1982), 156-184. | DOI | Zbl

[23] E. V. Gekeler - On regularity of small primes in functions fields, J. Number Theory 34 (1990), 114-127. | DOI | Zbl

[24] E. V. Gekeler - On finite Drinfeld Modules, J. Algebra 141 (1991), 187-203. | DOI | Zbl

[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. | Zbl

[26] D. Goss - Basic Structures of Function Field Arithmetic, Springer (1996). | MR | Zbl

[27] D. Goss - Separability, Multi-valued operators and zeros of L-functions, Prépub. (1997).

[28] D. Hayes - Explicit class field theory for rational function fields, Trans. Amer. Math. Soc. 189 (1974), 77-91. | DOI | MR | Zbl

[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. | MR | Zbl

[30] Y. Hellegouarch - Galois calculus and Carlitz exponentials, in The Arithmetic of Function Fields (éds D. Goss et al), De Gruyter (1992), 33-50. | MR | Zbl

[31] Y. Hellegouarch - Une généralisation d'un critère de de Mathan, C.R. Acad. Sci. Paris, t. 321, I (1995), 677-680. | MR | Zbl

[32] B. De Mathan - Irrationality measures and transcendance in positive characteristic, J. Number Theory 54 (1995), 93-112. | DOI | MR | Zbl

[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. | MR | Zbl

[34] O. Ore - On a Special class of polynomials, Trans. Amer. Math. Soc. 35 (1933), 559-584. | DOI | JFM | MR | Zbl

[35] O. Ore - Theory of non-commutative polynomials, Annals of Math. 34 (1933), 480-508. | DOI | JFM | MR | Zbl

[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. | MR | Zbl

[37] M. Rosen - The Hilbert class field in function fields, Expos. Math. 5 (1987), 365-378. | MR | Zbl

[38] F. B. Schultheis - Carlitz-Kummer function fields, J. Number Theory 36 (1990), 133-144. | DOI | MR | Zbl

[39] F. B. Schultheis - Explicit reciprocity laws in algebraic function fields, Thesis, UMT Ann Arbor, (1987).

[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. | MR | Zbl

[41] J.-P. Serre - Complex multiplication, in Algebraic Number Theory, J.W.S. Cassels and A. Fröhlich éds, Ac. Press, London, 1967. | MR | Zbl

[42] T. Takahashi - Good reduction of elliptic modules, J. Math. Soc. of Japan 34 (1982), 475-487. | DOI | MR | Zbl

[43] J. Tate - Number theoretic background, in Proceedings Symposia in Pure Mathematics 33, Part 2, Amer. Math. Soc. (1979), 3-26. | MR | Zbl

[44] D. Thakur - On characteristic p zeta functions, Compositio Math. 99 (1995), 231-247. | EuDML | Numdam | MR | Zbl

[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. | MR | Zbl

[46] L. Wade - Certain quantities transcendent over GF(pn,x) I, Duke Math. J. 8 (1941), 707-729. | DOI | MR | Zbl

[47] L. Wade - Certain quantities transcendent over GF(pn,x) II, Duke Math. J. 10 (1943), 587-594. | DOI | MR | Zbl

[48] M. Waldschmidt - Transcendence problems connected with Drinfeld modules, Istambul Üniv. Fen. Fak. Mat. Du. 49 (1990), 57-75. | MR | Zbl

[49] D. Wan - On the Riemann hypothesis for the characteristic p zeta function, J. Number Theory 58 (1996), 196-212. | DOI | MR | Zbl

[50] A. Weil - Basic Number Theory, Die Grundlehren der Mathematischen Wissenschaften 144, Springer (1967). | MR | Zbl

[51] J. Yu - Transcendence and special zeta-values in characteristic p, Ann. of Maths 134 (1991), 1-23. | DOI | Zbl

[52] J. Yu - Transcendence in finite characteristics, in The Arithmetic of Function Fields (éds. D. Goss et al) De Gruyter (1992), 253-264. | Zbl