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Comparison of 4-class ranks of certain quadratic fields

Author(s): Frank Gerth III
Journal: Proc. Amer. Math. Soc. 129 (2001), 2547-2552.
MSC (2000): Primary 11R11, 11R29, 11R45
Posted: January 23, 2001
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Abstract: Let $m$ be a square-free positive integer. Let $r_{4}(K)$ denote the 4-class rank of a quadratic field $K$. This paper examines how likely it is for $r_{4}(\mathbb{Q} (\sqrt {-m}\,)) =r_{4} (\mathbb{Q} (\sqrt {m}\,))$ and for $r_{4} (\mathbb{Q} (\sqrt {-m}\,)) = r_{4} (\mathbb{Q} (\sqrt {m}\,)) +1$.

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Additional Information:

Frank Gerth III
Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712-1082
Email: gerth@math.utexas.edu

DOI: 10.1090/S0002-9939-01-05922-6
PII: S 0002-9939(01)05922-6
Received by editor(s): January 19, 2000
Posted: January 23, 2001
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2001, American Mathematical Society

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