Simple proofs of the Siegel–Tatuzawa and Brauer–Siegel theorems
Tom 108 / 2007
Colloquium Mathematicum 108 (2007), 277-283
MSC: Primary 11R42; Secondary 11R29.
DOI: 10.4064/cm108-2-9
Streszczenie
We give a simple proof of the Siegel–Tatuzawa theorem according to which the residues at 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.
