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. doi:10.1515/crll.1982.332.156. https://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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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. | ||||||
Issue or Number: | 332 | ||||||
DOI: | 10.1515/crll.1982.332.156 | ||||||
Record Number: | CaltechAUTHORS:20180806-111756018 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180806-111756018 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 88600 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | Tony Diaz | ||||||
Deposited On: | 06 Aug 2018 18:31 | ||||||
Last Modified: | 16 Nov 2021 00:28 |
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