### Abstract

This article provides a formalisation of Beukers's straightforward analytic proof that ζ(3) is irrational. This was first proven by Apéry (which is why this result is also often called ‘Apéry's Theorem’) using a more algebraic approach. This formalisation follows Filaseta's presentation of Beukers's proof.

### License

BSD License

### Topics

- Mathematics/Number theory

### Session Zeta_3_Irrational

- Zeta_3_Irrational

### Depends on

- The Transcendence of e
- Elementary Facts About the Distribution of Primes
- The Prime Number Theorem

### Auto-related entries

- Metatheory of Q0
- Hello World
- Kleene Algebra with Tests and Demonic Refinement Algebras

## Cite

×

Zeta_3_Irrational-AFP

    @article{Zeta_3_Irrational-AFP,
      author  = {Manuel Eberl},
      title   = {The Irrationality of ζ(3)},
      journal = {Archive of Formal Proofs},
      month   = {December},
      year    = {2019},
      note    = {\url{https://isa-afp.org/entries/Zeta_3_Irrational.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

Download

## Download

× Download latest

Older releases:

- Sep 13, 2023 : Isabelle2023
- Oct 27, 2022 : Isabelle2022
- Dec 14, 2021 : Isabelle2021-1
- Feb 23, 2021 : Isabelle2021
- Apr 20, 2020 : Isabelle2020
- Dec 28, 2019 : Isabelle2019