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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A lower bound for the class numbers of abelian algebraic number fields with odd degree


Author: Mao Hua Le
Journal: Proc. Amer. Math. Soc. 123 (1995), 1347-1350
MSC: Primary 11R29; Secondary 11M20, 11R20, 11R42
MathSciNet review: 1249886
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Abstract: Let $ {\Delta _K},{h_K},{R_K}$ denote the discriminant, the class number, and the regulator of the Abelian algebraic number field $ K = \mathbb{Q}(\alpha )$ with degree d, respectively. In this note we prove that if $ d > 1,2\nmid d$, and the defining polynomial of $ \alpha $ has exactly $ {r_1}$ real zeros and $ {r_2}$ pairs of complex zeros, then $ {h_K} > w\sqrt {\vert{\Delta _K}\vert} /{2^{{r_1}}}{(2\pi )^{{r_2}}}33{R_K}\log 4\vert{\Delta _K}\vert$, where w is the number of roots of unity in K.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1249886-X
PII: S 0002-9939(1995)1249886-X
Article copyright: © Copyright 1995 American Mathematical Society