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Comparison of 4-class ranks of certain quadratic fields

Authors:	Frank Gerth III

Affiliation:	Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712-1082

Abstract:	Let be a square-free positive integer. Let $r_{4}(K)$ denote the 4-class rank of a quadratic field . 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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