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

• Autorzy: Stéphane R. Louboutin
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11R42: Zeta functions and L -functions of number fields
• 11R29: Class numbers, class groups, discriminants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 108
• Numer: 2
• Strony: 277-283

Daty

wydano

2007

Twórcy

autor

Stéphane R. Louboutin

• Institut de Mathématiques de Luminy, UMR 6206, 163, avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France

Identyfikatory

DOI

10.4064/cm108-2-9