×

p-adic interpolation of logarithmic derivatives associated to certain Lubin-Tate formal groups. (English) Zbl 0587.12007

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 \({\mathbb{Q}}_ p\), some results on p- adic interpolation developed by Kubota, Leopoldt, Iwasawa, Mazur, Katz and others notably for the multiplicative group \({\hat {\mathbb{G}}}_ m\), and which they used to construct p-adic L-functions.

MSC:

11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
14L05 Formal groups, \(p\)-divisible groups
11S40 Zeta functions and \(L\)-functions
PDFBibTeX XMLCite
Full Text: DOI Numdam EuDML

References:

[1] [1] , Valeurs aux entiers négatifs des fonctions zêta et fonctions zêta p-adiques, Inventiones Math., 51 (1979), 29-59. · Zbl 0408.12015
[2] [2] , Division values in local fields, Inventiones Math., 53 (1979), 91-116. · Zbl 0429.12010
[3] [3] , Lectures on p-adic L-functions, Annals of Math. Studies, 74 P.U.P. (1972). · Zbl 0236.12001
[4] [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] [5] and , Eine p-adische Theorie der Zetawerte, Crelle’s J, 214/215 (1964), 328-339. · Zbl 0186.09103
[6] [6] , Formal groups and p-adic interpolation, Astérisque, 41-42 (1977) 55-65. · Zbl 0351.14024
[7] [8] , Zur Struktur der l-Klassengruppe galoisscher Zahlkorper, J. reine angew. Math., 199 (1958), 165-174. · Zbl 0559.14032
[8] [5] , Bounded Analytic Functions, Academic Press, 1981. · Zbl 0395.12005
[9] [9] , Eine p-adiche Theorie der Zetewerte II, Crelle’s J., 274/275 (1975), 225-239. · Zbl 0309.12009
[10] [10] , On p-adic L-functions associated to elliptic curves, Inventiones Math., 56 (1980), 19-55. · Zbl 0425.12017
[11] [11] , One-parameter formal Lie groups over p-adic integer rings, Annals of Math., 80 (1964), 464-484. · Zbl 0135.07003
[12] [12] and , Arithmetic of Weil curves, Inventiones Math., 25 (1974), 1-61. · Zbl 0281.14016
[13] [11] , The order of singularity in Fuch’s theory, Math. Zeitshrift, 72 (1960), 379-398. · Zbl 0513.14012
[14] [14] , Formes modulaires et fonction zêta p-adiques, In Springer Lecture Notes in Math., 350 (1973), 191-268. · Zbl 0277.12014
[15] [15] , p-divisible groups, Proc. Conf. On local fields, ed. T. Springer, Springer-Verlag, (1967), 153-183. · Zbl 0157.27601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.