Apery's theorem is a result in number theory, proved by Roger Apery, stating that Apery's constant, the value of the Riemann zeta function at 3, is irrational, meaning it cannot be written as a ratio of two integers. The theorem stands apart from the situation at even integers, where the zeta function's values were already known to be irrational multiples of powers of pi; whether the zeta function takes irrational values at other odd integers beyond 3 remains an open question, although such irrationality is conjectured. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementThe value of the Riemann zeta function at 3, Apery's constant, is irrational. Roger Apery announced the result in June 1978 in a talk titled Sur l'irrationalite de zeta(3). 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Apery's theorem (Wikipedia)
Wikimedia FoundationHistory section, paragraph on the 1978 announcementQuote, History section, paragraph on the 1978 announcement
However, in June 1978, Roger Apéry gave a talk titled "Sur l'irrationalité de ΞΆ(3)."
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