Comparison of 4-class ranks of certain quadratic fields
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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 $r_{4} (\mathbb {Q} (\sqrt {-m} )) = r_{4} (\mathbb {Q} (\sqrt {m} )) +1$.References
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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
- Received by editor(s): January 19, 2000
- Published electronically: January 23, 2001
- Communicated by: David E. Rohrlich
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2547-2552
- MSC (2000): Primary 11R11, 11R29, 11R45
- DOI: https://doi.org/10.1090/S0002-9939-01-05922-6
- MathSciNet review: 1838376