Simple proofs of the Siegel-Tatuzawa and Brauer-Siegel theorems

Stéphane R. Louboutin. "Simple proofs of the Siegel-Tatuzawa and Brauer-Siegel theorems." Colloquium Mathematicae 108.2 (2007): 277-283. <http://eudml.org/doc/283504>.

@article{StéphaneR2007,
abstract = {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.},
author = {Stéphane R. Louboutin},
journal = {Colloquium Mathematicae},
keywords = {Dedekind zeta function; Siegel-Tatuzawa theorem; Brauer-Siegel theorem},
language = {eng},
number = {2},
pages = {277-283},
title = {Simple proofs of the Siegel-Tatuzawa and Brauer-Siegel theorems},
url = {http://eudml.org/doc/283504},
volume = {108},
year = {2007},
}

TY - JOUR
AU - Stéphane R. Louboutin
TI - Simple proofs of the Siegel-Tatuzawa and Brauer-Siegel theorems
JO - Colloquium Mathematicae
PY - 2007
VL - 108
IS - 2
SP - 277
EP - 283
AB - 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.
LA - eng
KW - Dedekind zeta function; Siegel-Tatuzawa theorem; Brauer-Siegel theorem
UR - http://eudml.org/doc/283504
ER -