generalization of the Brauer-Siegel bound? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T09:56:47Z http://mathoverflow.net/feeds/question/56158 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/56158/generalization-of-the-brauer-siegel-bound generalization of the Brauer-Siegel bound? genshin 2011-02-21T10:02:21Z 2011-02-21T10:02:21Z <p>For imaginary quadratic number fields $K$ of fundamental discriminant $-D$, the Brauer-Siegel theorem implies that the class number $h(D)$ of $K$ is "close" to $\sqrt{D}$, more precisely for any $c\in(0,1/2)$, there exists strictly positive constants $A_c$ and $B_c$ such that $$A_cD^{\frac{1}{2}-c}\leq h(D) \leq B_cD^{\frac{1}{2}+c}$$</p> <p>I'd like to know if similar results are known for more general fields, typically quadratic CM extensions of totally real fields. It seems that in the more general case additional inputs have to be included, such as regulators. Can one simply reduces the asymptotic case to some rational functions in discriminants?</p> <p>Thanks a lot!</p>