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On p-adic L-functions and cyclotomic fields

Published online by Cambridge University Press:  22 January 2016

Ralph Greenberg
Ralph Greenberg*
Affiliation:
University of Maryland, Brandeis University
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Let p be a prime. If one adjoins to Q all pn-th roots of unity for n = 1, 2, 3, …, then the resulting field will contain a unique subfield Q∞ such that Q∞ is a Galois extension of Q with Gal the additive group of p-adic integers. We will denote Gal(Q∞/Q) by Γ.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 56 , January 1975 , pp. 61 - 77
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1975

References

[1] Brumer, A., Travaux recents d’Iwasawa et de Leopoldt, Seminaire Bourbaki 325 (1967).Google Scholar
[2] Coates, J., Lichtenbaum, S., On l-adic zeta functions, Ann. of Math., 98 (1973), 498–550.CrossRefGoogle Scholar
[3] Coates, J., Sinnott, W., On p-adic L-functions over real quadratic fields, to appear.Google Scholar
[4] Greenberg, R., On a certain l-adic representation, Inventiones Math., 21 (1973), 247–254.CrossRefGoogle Scholar
[5] Greenberg, R., On the Iwasawa invariants of totally real number fields, to appear in Amer. J. of Math.Google Scholar
[6] Iwasawa, K., Some modules in the theory of cyclotomic fields, J. Math. Soc. Japan, 16 (1964), 42–82.CrossRefGoogle Scholar
[7] Iwasawa, K., On p-adic L-functions, Ann. of Math., 89 (1969), 198–205.CrossRefGoogle Scholar
[8] Iwasawa, K., Lectures on p-adic L-functions, Ann. Math. Studies 74, Princeton University Press, 1972.Google Scholar
[9] Iwasawa, K., On Zl -extensions of algebraic number fields, Ann. of Math., 98 (1973), 246–326.CrossRefGoogle Scholar
[10] Iwasawa, K., Computation of invariants in the theory of cyclotomic fields, J. Math. Soc. Japan, 18 (1966), 86–96.CrossRefGoogle Scholar
[11] Kubota, T., Leopoldt, H., Eine p-adische Theorie der Zetawerte (Teil I), J. Reine Angew. Math., 213 (1964), 328–339.Google Scholar
[12] Serre, J.-P., Formes modulaires et fonctions zeta p-adiques, Proceedings of Summer Institute on Modular Forms, vol. 3.Google Scholar
[13] Siegel, C. L., Über die analytische Theorie der quadratischen Formen III, Ann. of Math., 38 (1937), 212–291.CrossRefGoogle Scholar
[14] Stickelberger, L., Über eine Verallgemeinerung der Kreistheilung, Math. Ann., 37 (1890), 321–367.CrossRefGoogle Scholar