Simple proofs of the Siegel–Tatuzawa and Brauer–Siegel theorems
Volume 108 / 2007
Colloquium Mathematicum 108 (2007), 277-283
MSC: Primary 11R42; Secondary 11R29.
DOI: 10.4064/cm108-2-9
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.
