Abstract
The classical Brauer–Siegel theorem for number fields proved by Brauer (see [1]) claims that, if k ranges over a sequence of number fields normal over Q and such that nk/ log |Dk| → 0, then log(hkRk)/ log √ |Dk| → 1. Here Dk, hk, and Rk stand for the discriminant, the class number, and the regulator of the field k, respectively. This theorem was generalized by M. A. Tsfasman and S. G. Vlăduţ (see [2]) to the case in which the condition nk/ log |Dk| → 0 fails to hold (asymptotically good families of fields). Here the limit thus obtained, lim log(hkRk)/ log √ |Dk|, need not be equal to 1.
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