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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the exponent of the ideal class groups of complex quadratic fields.


Authors: David W. Boyd and H. Kisilevsky
Journal: Proc. Amer. Math. Soc. 31 (1972), 433-436
DOI: https://doi.org/10.1090/S0002-9939-1972-0289454-4
MathSciNet review: 0289454
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Abstract | References | Additional Information

Abstract: Let $ m(d)$ denote the exponent of the ideal class group of the complex quadratic field $ Q(\surd d)$, where $ d < 0$ is a fundamental discriminant. It is shown that there are only finitely many $ d$ for which $ m(d) = 3$. Assuming the extended Riemann Hypothesis, it is shown that $ m(d) \to \infty {\text{ as }}\vert d\vert \to \infty $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0289454-4
Keywords: Complex quadratic field, ideal class group, least prime quadratic residue, extended Riemann Hypothesis
Article copyright: © Copyright 1972 American Mathematical Society