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Density results for the 2-classgroups of imaginary quadratic fields

Morton, Patrick (1982) Density results for the 2-classgroups of imaginary quadratic fields. Journal für die reine und angewandte Mathematik, 1982 (332). pp. 156-187. ISSN 1435-5345. http://resolver.caltech.edu/CaltechAUTHORS:20180806-111756018

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Abstract

In one of the long series of papers, Rédie [15] has given a theoretical description of the first three ‘levels’ of the 2-classgroup of a quadratic number field. Starting from Reichardt’s characterization [18] of the 2^n-rank (which we done by e_(2n)) of the restriced classgroup L of the field Q(1√4), Rédie characterized e_4 and e_8 in terms of certain factorizations of Δ and a 2-valued multiplicative symbol {a_1, a_2, a_3}. This symbol is closely related to the splitting of primes in eight degree extensions of Q (see [2]). Using this symbol, Rédie was able to prove that there are infinitely many real quadratic fields for which e_2, e_4, and e_8 have arbitrarily assigned values.


Item Type:Article
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https://doi.org/10.1515/crll.1982.332.156DOIArticle
Additional Information:© 1982 by Walter de Gruyter GmbH. The contents of this paper are taken from the author’s doctoral dissertation, submitted to the Rackham School of Graduate Studies, University of Michigan, 1979.
Record Number:CaltechAUTHORS:20180806-111756018
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180806-111756018
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ID Code:88600
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Deposited By: Tony Diaz
Deposited On:06 Aug 2018 18:31
Last Modified:06 Aug 2018 18:31

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