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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Lower bounds for relative class numbers of CM-fields
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by Stéphane Louboutin PDF
Proc. Amer. Math. Soc. 120 (1994), 425-434 Request permission


Let ${\mathbf {K}}$ be a CM-field that is a quadratic extension of a totally real number field ${\mathbf {k}}$. Under a technical assumption, we show that the relative class number of ${\mathbf {K}}$ is large compared with the absolute value of the discriminant of ${\mathbf {K}}$, provided that the Dedekind zeta function of ${\mathbf {k}}$ has a real zero $s$ such that $0 < s < 1$. This result will enable us to get sharp upper bounds on conductors of totally imaginary abelian number fields with class number one or with prescribed ideal class groups.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 120 (1994), 425-434
  • MSC: Primary 11R42; Secondary 11R29
  • DOI:
  • MathSciNet review: 1169041