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The class number of the field of $ 5\sp{n}$th roots of unity


Author: Lawrence C. Washington
Journal: Proc. Amer. Math. Soc. 61 (1976), 205-208
MSC: Primary 12A50; Secondary 12A35
DOI: https://doi.org/10.1090/S0002-9939-1976-0424752-6
MathSciNet review: 0424752
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Abstract: Let $ h_n^ - $ be the relative class number of the field of $ {5^n}$th roots of unity. If $ l$ is any prime number, then the $ l$-part of $ h_n^ - $ is bounded independent of $ n$.


References [Enhancements On Off] (What's this?)

  • [1] H. Hasse, Über die Klassenzahl abelscher Zahlkörper, Akademie-Verlag, Berlin, 1952. MR 14, 141. MR 0049239 (14:141a)
  • [2] K. Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg 20 (1956), 257-258. MR 18, 644. MR 0083013 (18:644d)
  • [3] S. Lang, Algebra, Addison-Wesley, Reading, Mass., 1965. MR 33 #5416. MR 0197234 (33:5416)
  • [4] L. Washington, Class numbers and $ {{\mathbf{Z}}_p}$-extensions, Math. Ann. 214 (1975), 177-193. MR 51 #437. MR 0364182 (51:437)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0424752-6
Article copyright: © Copyright 1976 American Mathematical Society

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