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.
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)
Principal Result Of
Source Roger Apéry (Wikipedia)
Proved By
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.
View the Source Roger Apéry (Wikipedia)
Principal Result Of: Roger Apéry, LeadQuote, Principal Result Of: Roger Apéry, Lead
most remembered for Apéry's theorem
Apery's Theorem (Wikipedia)
Proved By: Roger Apéry, Lead sentenceQuote, Proved By: Roger Apéry, Lead sentence
The theorem is named after Roger Apéry.
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