p -adic interpolation of logarithmic derivatives associated to certain Lubin-Tate formal groups

John L. Boxall

Annales de l'institut Fourier (1986)

  • Volume: 36, Issue: 3, page 1-27
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Boxall, John L.. "$p$-adic interpolation of logarithmic derivatives associated to certain Lubin-Tate formal groups." Annales de l'institut Fourier 36.3 (1986): 1-27. <http://eudml.org/doc/74724>.

@article{Boxall1986,
abstract = {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 $\{\bf Q\}_ p$, some results on $p$-adic interpolation developed by Kubota, Leopoldt, Iwasawa, Mazur, Katz and others notably for the multiplicative group $\{\hat\{\bf G\}\}_ m$, and which they used to construct $p$-adic $L$-functions.},
author = {Boxall, John L.},
journal = {Annales de l'institut Fourier},
keywords = {logarithmic derivatives; commutative formal groups; p-adic interpolation; p-adic L-functions},
language = {eng},
number = {3},
pages = {1-27},
publisher = {Association des Annales de l'Institut Fourier},
title = {$p$-adic interpolation of logarithmic derivatives associated to certain Lubin-Tate formal groups},
url = {http://eudml.org/doc/74724},
volume = {36},
year = {1986},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 36
IS - 3
SP - 1
EP - 27
AB - 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 ${\bf Q}_ p$, some results on $p$-adic interpolation developed by Kubota, Leopoldt, Iwasawa, Mazur, Katz and others notably for the multiplicative group ${\hat{\bf G}}_ m$, and which they used to construct $p$-adic $L$-functions.
LA - eng
KW - logarithmic derivatives; commutative formal groups; p-adic interpolation; p-adic L-functions
UR - http://eudml.org/doc/74724
ER -

References

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  1. [1] P. CASSOU-NOGUES, Valeurs aux entiers négatifs des fonctions zêta et fonctions zêta p-adiques, Inventiones Math., 51 (1979), 29-59. Zbl0408.12015MR80h:12009b
  2. [2] R.F. COLEMAN, Division values in local fields, Inventiones Math., 53 (1979), 91-116. Zbl0429.12010MR81g:12017
  3. [3] K. IWASAWA, Lectures on p-adic L-functions, Annals of Math. Studies, 74 P.U.P. (1972). Zbl0236.12001MR50 #12974
  4. [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. [5] T. KUBOTA and H.W. LEOPOLDT, Eine p-adische Theorie der Zetawerte, Crelle's J, 214/215 (1964), 328-339. Zbl0186.09103MR29 #1199
  6. [6] N. KATZ, Formal groups and p-adic interpolation, Astérisque, 41-42 (1977) 55-65. Zbl0351.14024MR56 #319
  7. [7] N. KATZ, Divisibilities, congruences and Cartier duality, J. Fac. Sci. Univ. Tokyo, Ser. 1 A, 28 (1982), 667-678. Zbl0559.14032
  8. [8] S. LANG, Cyclotomic fields, Graduate texts in Math, Springer-Verlag (1978). Zbl0395.12005MR58 #5578
  9. [9] H.W. LEOPOLDT, Eine p-adiche Theorie der Zetewerte II, Crelle's J., 274/275 (1975), 225-239. 
  10. [10] S. LICHTENBAUM, On p-adic L-functions associated to elliptic curves, Inventiones Math., 56 (1980), 19-55. Zbl0425.12017MR81j:12013
  11. [11] J. LUBIN, One-parameter formal Lie groups over p-adic integer rings, Annals of Math., 80 (1964), 464-484. Zbl0135.07003MR29 #5827
  12. [12] B. MAZUR and P. SWINNERTON-DYER, Arithmetic of Weil curves, Inventiones Math., 25 (1974), 1-61. Zbl0281.14016MR50 #7152
  13. [13] K. RUBIN, Congruences for special values of L-functions of elliptic curves with complex multiplication, Inventiones Math., 71 (1983), 339-364. Zbl0513.14012MR84h:12018
  14. [14] J.P. SERRE, Formes modulaires et fonction zêta p-adiques, In Springer Lecture Notes in Math., 350 (1973), 191-268. Zbl0277.12014MR53 #7949a
  15. [15] J. TATE, p-divisible groups, Proc. Conf. On local fields, ed. T. Springer, Springer-Verlag, (1967), 153-183. Zbl0157.27601

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