Herbrand-Ribet theorem (English, name)
expansion: the Herbrand-Ribet theorem
Senses:
topics: mathematics
sciences
glosses: 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.
Forms:
form: the Herbrand-Ribet theorem
tags: canonical