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

 

On the exponent of the ideal class group of $ {\bf Q}(\sqrt{-d})$


Author: Francesco Pappalardi
Journal: Proc. Amer. Math. Soc. 123 (1995), 663-671
MSC: Primary 11R29; Secondary 11N69, 11R11, 11R47
MathSciNet review: 1233979
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Abstract: Let $ m(d)$ be the exponent of the ideal class group of $ {\mathbf{Q}}(\sqrt { - d} )$, we establish the bound $ m(d) \gg \frac{{\log d}}{{\log \log d}}$ for almost all the discriminants d by using uniform asymptotic formulas on the number of $ n \leq x$ for which there exists a prime less than s for which n is a quadratic residue.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1233979-7
PII: S 0002-9939(1995)1233979-7
Keywords: Complex quadratic fields, ideal class group, least prime quadratic residue
Article copyright: © Copyright 1995 American Mathematical Society