English Explanatory Dictionary

Herbrand-Ribet theorem

English dictionary entry

Meanings

name
  1. 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.

Word forms

Herbrand-Ribet theorem the Herbrand-Ribet theorem

Etymology

Named after Jacques Herbrand and Kenneth Ribet.

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