Speakur

Word Pronunciation & Dictionary

herbrand-ribet theorem

Word Rarity Very rare

Frequency: Zipf frequency 1.07 in modern English

Syllables
her-brand-ri-bet the-o-rem
IPA
33
Scrabble Score
20
Letters
6
Syllables
11
Unique Chars

Meaning

name

A result on the class group of certain number fields, strengthening Ernst Kummer's theorem to the effect that the prime p divides the class number of the cyclotomic field of p-th roots of unity iff p divides the numerator of the n-th Bernoulli number Bₙ for some n, 0 < n < p − 1. The Herbrand–Ribet theorem specifies what, in particular, it means when p divides such an Bₙ.

Etymology

Named after Jacques Herbrand and Kenneth Ribet.

Inflected Forms

the Herbrand-Ribet theorem (canonical)

Questions

What does herbrand-ribet theorem mean?
A result on the class group of certain number fields, strengthening Ernst Kummer's theorem to the effect that the prime p divides the class number of the cyclotomic field of p-th roots of unity iff p divides the numerator of the n-th Bernoulli number Bₙ for some n, 0 < n < p − 1. The Herbrand–Ribet theorem specifies what, in particular, it means when p divides such an Bₙ.
Where does herbrand-ribet theorem come from?
Named after Jacques Herbrand and Kenneth Ribet.

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