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
In Branch
Source Apery's theorem (Wikipedia)
Sources
1. Apery's theorem (Wikipedia)
Wikimedia FoundationHistory section, paragraph on the 1978 announcement
However, in June 1978, Roger Apéry gave a talk titled "Sur l'irrationalité de ζ(3)."
In Branch: Number Theory, Lead paragraph
In mathematics, Apéry's theorem is a result in number theory which states that Apéry's constant ζ(3) is irrational.
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