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

Volume 108 / 2007

Stéphane R. Louboutin Colloquium Mathematicum 108 (2007), 277-283 MSC: Primary 11R42; Secondary 11R29. DOI: 10.4064/cm108-2-9


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.


  • Stéphane R. LouboutinInstitut de Mathématiques de Luminy, UMR 6206
    163, avenue de Luminy, Case 907
    13288 Marseille Cedex 9, France

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