Le but de cet article est de généraliser à certains groupes formels, commutatifs, de dimension un, de hauteur supérieure à un et définis sur l’anneau des entiers d’une extension finie de , quelques résultats sur l’interpolation -adique développés par Kubota, Leopoldt, Iwasawa, Mazur, Katz et d’autres, notamment pour le groupe multiplicatif , dont se sont servis ces auteurs pour la construction des fonctions -adiques.
The purpose of this paper is to generalize, to certain commutative formal groups of dimension one and height greater than one defined over the ring of integers of a finite extension of , some results on -adic interpolation developed by Kubota, Leopoldt, Iwasawa, Mazur, Katz and others notably for the multiplicative group , and which they used to construct -adic -functions.
@article{AIF_1986__36_3_1_0, author = {Boxall, John L.}, title = {$p$-adic interpolation of logarithmic derivatives associated to certain Lubin-Tate formal groups}, journal = {Annales de l'Institut Fourier}, volume = {36}, year = {1986}, pages = {1-27}, doi = {10.5802/aif.1056}, mrnumber = {88f:11113}, zbl = {0587.12007}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1986__36_3_1_0} }
Boxall, John L. $p$-adic interpolation of logarithmic derivatives associated to certain Lubin-Tate formal groups. Annales de l'Institut Fourier, Tome 36 (1986) pp. 1-27. doi : 10.5802/aif.1056. http://gdmltest.u-ga.fr/item/AIF_1986__36_3_1_0/
[1] Valeurs aux entiers négatifs des fonctions zêta et fonctions zêta p-adiques, Inventiones Math., 51 (1979), 29-59. | MR 80h:12009b | Zbl 0408.12015
,[2] Division values in local fields, Inventiones Math., 53 (1979), 91-116. | MR 81g:12017 | Zbl 0429.12010
,[3] Lectures on p-adic L-functions, Annals of Math. Studies, 74 P.U.P. (1972). | MR 50 #12974 | Zbl 0236.12001
,[4] Uber eine allgemeine Eigenschaft der rationale Entwicklungscoefficienten eines bestimmten Gattung analytischer Functionen, Crelle's J., 41 (1851) 368-372, (= collected works vol. 1, pp. 358-362, Springer-Verlag (1975)).
,[5] Eine p-adische Theorie der Zetawerte, Crelle's J, 214/215 (1964), 328-339. | MR 29 #1199 | Zbl 0186.09103
and ,[6] Formal groups and p-adic interpolation, Astérisque, 41-42 (1977) 55-65. | MR 56 #319 | Zbl 0351.14024
,[7] Divisibilities, congruences and Cartier duality, J. Fac. Sci. Univ. Tokyo, Ser. 1 A, 28 (1982), 667-678. | Zbl 0559.14032
,[8] Cyclotomic fields, Graduate texts in Math, Springer-Verlag (1978). | MR 58 #5578 | Zbl 0395.12005
,[9] Eine p-adiche Theorie der Zetewerte II, Crelle's J., 274/275 (1975), 225-239.
,[10] On p-adic L-functions associated to elliptic curves, Inventiones Math., 56 (1980), 19-55. | MR 81j:12013 | Zbl 0425.12017
,[11] One-parameter formal Lie groups over p-adic integer rings, Annals of Math., 80 (1964), 464-484. | MR 29 #5827 | Zbl 0135.07003
,[12] Arithmetic of Weil curves, Inventiones Math., 25 (1974), 1-61. | MR 50 #7152 | Zbl 0281.14016
and ,[13] Congruences for special values of L-functions of elliptic curves with complex multiplication, Inventiones Math., 71 (1983), 339-364. | MR 84h:12018 | Zbl 0513.14012
,[14] Formes modulaires et fonction zêta p-adiques, In Springer Lecture Notes in Math., 350 (1973), 191-268. | MR 53 #7949a | Zbl 0277.12014
,[15] p-divisible groups, Proc. Conf. On local fields, ed. T. Springer, Springer-Verlag, (1967), 153-183. | Zbl 0157.27601
,