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On p-adic L-functions and elliptic units

Published online by Cambridge University Press:  09 April 2009

J. Coates
Affiliation:
Department of Mathematics Institute of Advanced Studies Australian National UniversityCanberra, Australia
A. Wiles
Affiliation:
Department of Mathematics Harvard UniversityCambridge, Mass. 02138, USA
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Abstract

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The aim of the paper is to prove an elliptic analogue of a deep theorem of Iwasawa on cyclotomic fields.

Subject classification(Amer. Math. Soc. (MOS) 1970): primary 12 A 35, 12 A 65.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1978

References

Cassou-Nogues, P. (to appear), “p-adic L-functions for elliptic curves with complex multiplication I.”Google Scholar
Coates, J. (1977), “p-adic L-functions and Iwasawa's theory”, in Algebraic Number Fields, edited by Frohlich, A. (Academic Press, New York).Google Scholar
Coates, J. and Wiles, A. (1977), “On the conjecture of Birch and Swinnerton-Dyer”, Invent. Math. 39, 223251.CrossRefGoogle Scholar
Coleman, R. (to appear), “Some modules attached to Lubin-Tate groups”.Google Scholar
Iwasawa, K. (1964), “On some modules in the theory of cyclotomic fields”, J. Math. Soc. Japan 16, 4282.CrossRefGoogle Scholar
Iwasawa, K. (1969), “On p-adic L-functions”, Ann. Math. 89, 198205.CrossRefGoogle Scholar
Katz, N. (1977), “The Eisenstein measure and p-adic interpolation”, Amer. J. Math. 99, 238311.CrossRefGoogle Scholar
Katz, N. (1977), “Formal groups and p-adic interpolation”, Asterisque 41–42, 5565.Google Scholar
Lang, S., Introduction to Cyclotomic Fields (to be published by Springer Verlag).Google Scholar
Leopoldt, H. (1975), “Eine p-adische Theorie der Zetawerte II”, J. reine angew. Math. 274–275, 224239.Google Scholar
Lichtenbaum, S. (to appear), “On p-adic L-functions associated to elliptic curves’.Google Scholar
Lubin, J. (1964), ‘One parameter formal Lie groups over p-adic integer rings”, Ann. Math. 80, 464484.CrossRefGoogle Scholar
Manin, J. and Vishik, M. (1974), ‘p-adic Hecke series for imaginary quadratic fields”, Math. Sbornik 95, 357383.Google Scholar
Robert, G. (1973), “Unités elliptiques”, Bull. Soc. Math. France Mémoire 36.Google Scholar
Shimura, G. (1971), Introduction to the Arthmetic Theory of Automorphic Functions (Pub. Math. Soc. Japan) 11, 1971.Google Scholar
Wiles, A. (1978), “Higher explicit reciprocity laws”, Ann. Math., 107, 235254.CrossRefGoogle Scholar