The Brauer-Siegel theorem, obtained by Richard Brauer and Carl Ludwig Siegel, is an asymptotic result in algebraic number theory describing the behavior of a growing sequence of number fields. It generalizes results already known about the class numbers of imaginary quadratic fields to a broader sequence of fields, relating the product of each field's class number and regulator to its discriminant in the limit, under the assumption that each field is a Galois extension of the rational numbers and that the fields' degrees stay small relative to the logarithm of their discriminants. The result is not effective, meaning it does not by itself supply a usable numerical bound, though effective versions in the same direction were later initiated by Harold Stark in the early 1970s.
Facts
Partially Attested
Proof YearYear is from the References section citing Brauer's 1947 paper, not a body statement of the proof date StatementThe Brauer-Siegel theorem is an asymptotic result on the behaviour of algebraic number fields, generalising results known on the class numbers of imaginary quadratic fields to a more general sequence of number fields. 1 Classification
Statement FormCharacterization Theorem 1 Brauer-Siegel Theorem
Filter Results1 entry
Connections
Has Statement Form
In Branch
Source Brauer-Siegel theorem (Wikipedia)
Principal Result Of
Source Brauer-Siegel Theorem (Wikipedia)
Source Brauer-Siegel Theorem (Wikipedia)
Proved By
Source Brauer-Siegel theorem (Wikipedia)
Sources
1. Brauer-Siegel theorem (Wikipedia)
Introduction
is an asymptotic result on the behaviour of algebraic number fields
References
Richard Brauer, On the Zeta-Function of Algebraic Number Fields, American Journal of Mathematics 69 (1947), 243-250.
Proved By: Carl Ludwig Siegel, Lead paragraph
In mathematics, the Brauer-Siegel theorem, named after Richard Brauer and Carl Ludwig Siegel, is an asymptotic result on the behaviour of algebraic number fields, obtained by Richard Brauer and Carl Ludwig Siegel.
In Branch: Algebraic Number Theory, Lead paragraph
In mathematics, the Brauer-Siegel theorem, named after Richard Brauer and Carl Ludwig Siegel, is an asymptotic result on the behaviour of algebraic number fields, obtained by Richard Brauer and Carl Ludwig Siegel.
View the SourceBrauer-Siegel Theorem (Wikipedia)
Principal Result Of: Richard Brauer, Lead sentence of the article on the result
In mathematics, the Brauer-Siegel theorem, named after Richard Brauer and Carl Ludwig Siegel, is an asymptotic result on the behaviour of algebraic number fields, obtained by Richard Brauer and Carl Ludwig Siegel.
Principal Result Of: Carl Ludwig Siegel, Lead sentence of the article on the result
In mathematics, the Brauer-Siegel theorem, named after Richard Brauer and Carl Ludwig Siegel, is an asymptotic result on the behaviour of algebraic number fields, obtained by Richard Brauer and Carl Ludwig Siegel.
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.