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The Brauer-Siegel and Tsfasman-Vladut Theorems for Almost Normal Extensions of Number Fields | Alexey Zykin
; | Date: |
4 Nov 2004 | Subject: | Number Theory; Algebraic Geometry MSC-class: 11R29 | math.NT math.AG | Abstract: | The classical Brauer-Siegel theorem states that if $k$ runs through the sequence of normal extensions of $mathbb{Q}$ such that $n_k/log|D_k| o 0,$ then $log h_k R_k/log sqrt{|D_k|} o 1.$ First, in this paper we obtain the generalization of the Brauer-Siegel and Tsfasman-Vlu{a}duc{t} theorems to the case of almost normal number fields. Second, using the approach of Hajir and Maire, we construct several new examples concerning the Brauer-Siegel ratio in asymptotically good towers of number fields. These examples give smaller values of the Brauer-Siegel ratio than those given by Tsfasman and Vlu{a}duc{t} | Source: | arXiv, math.NT/0411099 | Other source: | [GID 597576] math.NT/0411099 | Services: | Forum | Review | PDF | Favorites |
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