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

Tom 108 / 2007

Stéphane R. Louboutin 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 $s=1$ 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.

Autorzy

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

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek