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
Abstract:
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.References
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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: https://doi.org/10.1090/S0002-9939-1994-1169041-0
- MathSciNet review: 1169041