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Ideal class groups in basic \(\mathbb Z_{p_1}\times\dots\times\mathbb Z_{p_s}\)-extensions of abelian number fields. (English) Zbl 0495.12007

MSC:
11R23 Iwasawa theory
11R18 Cyclotomic extensions
11R29 Class numbers, class groups, discriminants
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References:
[1] Ferrero, B., Washington, L.: The Iwasawa invariant ? p vanishes for abelian number fields. Ann. of Math.109, 377-395 (1979) · Zbl 0443.12001 · doi:10.2307/1971116
[2] Greenberg, R.: On the Iwasawa invariants of totally real number fields. Amer. J. Math.98, 263-284 (1976) · Zbl 0334.12013 · doi:10.2307/2373625
[3] Iwasawa, K.: On ?-extensions of algebraic number fields. Bull. Amer. Math. Soc.65, 183-226 (1959) · Zbl 0089.02402 · doi:10.1090/S0002-9904-1959-10317-7
[4] Iwasawa, K.: Lectures onp-adicL-functions. Ann. of Math. Studies No.74. Princeton: Princeton University Press, 1972
[5] Iwasawa, K.: On ? l of algebraic number fields. Ann. of Math.98, 246-326 (1973) · Zbl 0285.12008 · doi:10.2307/1970784
[6] Iwasawa, K.: On the ?-invariants of ? l -extensions. In: Number Theory, Algebraic Geometry and Commutative Algebra. In honor of Y. Akizuki, pp. 1-11. Tokyo: Kinokuniya 1973
[7] Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. New York: Wiley-Interscience 1974 · Zbl 0281.10001
[8] Lang, S.: Cyclotomic Fields. Berlin Heidelberg New York: Springer 1978 · Zbl 0395.12005
[9] Lang, S.: Cyclotomic Fields II. Berlin Heidelberg New York: Springer 1980 · Zbl 0435.12001
[10] Oesterlé, J.: Travaux de Ferrero et Washington sur le nombre de classes d’idéaux des corps cyclotomiques. Sém. Bourbaki,535, 1-13 (1979). Also in Springer Lecture Notes in Math.770, 170-182 (1980)
[11] Serre, J.P.: Classes des corps cyclotomiques (d’après K. Iwasawa). Sém. Bourbaki,174, 1-11 (1958)
[12] Washington, L.: Class numbers and ? p -extensions. Math. Ann.214, 177-193 (1975) · Zbl 0302.12007 · doi:10.1007/BF01352651
[13] Washington, L.: The non-p-part of the class number in a cyclotomic ? p -extensions. Invent. Math.49, 87-97 (1978) · Zbl 0403.12007 · doi:10.1007/BF01399512
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