We give a simple proof of the Siegel-Tatuzawa theorem according to which the residues at s = 1 of the Dedekind zeta functions of quadratic number fields are effectively not too small, with at most one exceptional quadratic field. We then give a simple proof of the Brauer-Siegel theorem for normal number fields which gives the asymptotics for the logarithm of the product of the class number and the regulator of number fields.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-2-9,
author = {St\'ephane R. Louboutin},
title = {Simple proofs of the Siegel-Tatuzawa and Brauer-Siegel theorems},
journal = {Colloquium Mathematicae},
volume = {107},
year = {2007},
pages = {277-283},
zbl = {1114.11090},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-2-9}
}
Stéphane R. Louboutin. Simple proofs of the Siegel-Tatuzawa and Brauer-Siegel theorems. Colloquium Mathematicae, Tome 107 (2007) pp. 277-283. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-2-9/