The Brauer-Siegel and Tsfasman-Vladut Theorems for Almost Normal Extensions of Number Fields
Zykin, Alexey
HAL, hal-00003222 / Harvested from HAL
Text on HAL
The classical Brauer-Siegel theorem states that if $k$ runs through the sequence of normal extensions of $\mathbb{Q}$ such that $n_k/\log|D_k|\to 0,$ then $\log h_k R_k/\log \sqrt{|D_k|}\to 1.$ First, in this paper we obtain the generalization of the Brauer-Siegel and Tsfasman-Vl\u{a}du\c{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 Vl\u{a}du\c{t}
Publié le : 2004-11-04
Classification:  Global field,  Brauer-Siegel theorem,  asymptotically good tower,  asymptotically bad tower,  11R29,  [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT],  [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG] 
@article{hal-00003222,
     author = {Zykin, Alexey},
     title = {The Brauer-Siegel and Tsfasman-Vladut Theorems for Almost Normal Extensions of Number Fields},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00003222}
}

Zykin, Alexey. The Brauer-Siegel and Tsfasman-Vladut Theorems for Almost Normal Extensions of Number Fields. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00003222/