Herbrand-Ribet theorem

proper noun

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.

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Meanings

proper nounthe Herbrand-Ribet theorem
  1. mathematicsA 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.

Origin

Named after Jacques Herbrand and Kenneth Ribet.

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Cite this entry
APA

Herbrand-Ribet theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Herbrand-Ribet%20theorem

MLA

“Herbrand-Ribet theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Herbrand-Ribet%20theorem. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Herbrand-Ribet theorem,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Herbrand-Ribet%20theorem.

Source: Herbrand-Ribet theorem on Wiktionary, CC BY-SA 4.0.