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Class numbers and \(\mathbb Z_p\)-extensions. (English) Zbl 0302.12007

MSC:
11R29 Class numbers, class groups, discriminants
11R23 Iwasawa theory
11R20 Other abelian and metabelian extensions
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References:
[1] Brauer, R.: On the zeta-functions of algebraic number fields. II. Am. J. Math.72, 739-746 (1950) · Zbl 0038.17602 · doi:10.2307/2372290
[2] Goldstein, L. J.: On the class numbers of cyclotomic fields. J. Number Theory5, 58-63 (1973) · Zbl 0253.12013 · doi:10.1016/0022-314X(73)90058-9
[3] Hasse, H.: Über die Klassenzahl abelscher Zahlkörper. Berlin: Akademie-Verlag 1952 · Zbl 0063.01966
[4] Iwasawa, K.: Lectures onp-adicL-functions. Princeton, Princeton Univ. Press 1972
[5] Iwasawa, K.: On ? l -extensions of algebraic number fields, Ann. 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, Kinokuniya, Tokyo, 1-11 1973
[7] Lang, S.: Algebraic number theory. Reading, Mass.: Addison-Wesley 1970 · Zbl 0211.38404
[8] Yokoi, H.: On the class number of a relatively cyclic number field. Nagoya Math. J.29, 31-44 (1967) · Zbl 0166.05803
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