p-adic interpolation of logarithmic derivatives associated to certain Lubin-Tate formal groups
Annales de l'Institut Fourier, Tome 36 (1986) no. 3, pp. 1-27.

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 Q p , quelques résultats sur l’interpolation p-adique développés par Kubota, Leopoldt, Iwasawa, Mazur, Katz et d’autres, notamment pour le groupe multiplicatif G ^ m , dont se sont servis ces auteurs pour la construction des fonctions L p-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 Q p , some results on p-adic interpolation developed by Kubota, Leopoldt, Iwasawa, Mazur, Katz and others notably for the multiplicative group G ^ m , and which they used to construct p-adic L-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},
     pages = {1--27},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {36},
     number = {3},
     year = {1986},
     doi = {10.5802/aif.1056},
     mrnumber = {88f:11113},
     zbl = {0587.12007},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.1056/}
}
TY  - JOUR
AU  - Boxall, John L.
TI  - $p$-adic interpolation of logarithmic derivatives associated to certain Lubin-Tate formal groups
JO  - Annales de l'Institut Fourier
PY  - 1986
SP  - 1
EP  - 27
VL  - 36
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - http://archive.numdam.org/articles/10.5802/aif.1056/
DO  - 10.5802/aif.1056
LA  - en
ID  - AIF_1986__36_3_1_0
ER  - 
%0 Journal Article
%A Boxall, John L.
%T $p$-adic interpolation of logarithmic derivatives associated to certain Lubin-Tate formal groups
%J Annales de l'Institut Fourier
%D 1986
%P 1-27
%V 36
%N 3
%I Institut Fourier
%C Grenoble
%U http://archive.numdam.org/articles/10.5802/aif.1056/
%R 10.5802/aif.1056
%G en
%F 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) no. 3, pp. 1-27. doi : 10.5802/aif.1056. http://archive.numdam.org/articles/10.5802/aif.1056/

[1] P. Cassou-Nogues, Valeurs aux entiers négatifs des fonctions zêta et fonctions zêta p-adiques, Inventiones Math., 51 (1979), 29-59. | MR | Zbl

[2] R.F. Coleman, Division values in local fields, Inventiones Math., 53 (1979), 91-116. | MR | Zbl

[3] K. Iwasawa, Lectures on p-adic L-functions, Annals of Math. Studies, 74 P.U.P. (1972). | MR | Zbl

[4] E.E. Kummer, 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] T. Kubota and H.W. Leopoldt, Eine p-adische Theorie der Zetawerte, Crelle's J, 214/215 (1964), 328-339. | MR | Zbl

[6] N. Katz, Formal groups and p-adic interpolation, Astérisque, 41-42 (1977) 55-65. | Numdam | MR | Zbl

[7] N. Katz, Divisibilities, congruences and Cartier duality, J. Fac. Sci. Univ. Tokyo, Ser. 1 A, 28 (1982), 667-678. | Zbl

[8] S. Lang, Cyclotomic fields, Graduate texts in Math, Springer-Verlag (1978). | MR | Zbl

[9] H.W. Leopoldt, Eine p-adiche Theorie der Zetewerte II, Crelle's J., 274/275 (1975), 225-239.

[10] S. Lichtenbaum, On p-adic L-functions associated to elliptic curves, Inventiones Math., 56 (1980), 19-55. | MR | Zbl

[11] J. Lubin, One-parameter formal Lie groups over p-adic integer rings, Annals of Math., 80 (1964), 464-484. | MR | Zbl

[12] B. Mazur and P. Swinnerton-Dyer, Arithmetic of Weil curves, Inventiones Math., 25 (1974), 1-61. | MR | Zbl

[13] K. Rubin, Congruences for special values of L-functions of elliptic curves with complex multiplication, Inventiones Math., 71 (1983), 339-364. | MR | Zbl

[14] J.P. Serre, Formes modulaires et fonction zêta p-adiques, In Springer Lecture Notes in Math., 350 (1973), 191-268. | MR | Zbl

[15] J. Tate, p-divisible groups, Proc. Conf. On local fields, ed. T. Springer, Springer-Verlag, (1967), 153-183. | Zbl

Cité par Sources :