Reseña: A formal proof of the irrationality of ζ(3)
Se ha publicado un artículo de razonamiento formalizado sobre teoría de números titulado A formal proof of the irrationality of ζ(3).
Sus autores son
- Assia Mahboubi (del grupo Gallinette en el Inria) y
- Thomas Sibut-Pinote (del INRIA Team SpecFun y la Université Paris-Saclay)
Su resumen es
This paper presents a complete formal verification of a proof that the evaluation of the Riemann zeta function at 3 is irrational, using the Coq proof assistant. This result was first presented by Apéry in 1978, and the proof we have formalized essentially follows the path of his original presentation. The crux of this proof is to establish that some sequences satisfy a common recurrence. We formally prove this result by an a posteriori verification of calculations performed by computer algebra algorithms in a Maple session. The rest of the proof combines arithmetical ingredients and asymptotic analysis, which we conduct by extending the Mathematical Components libraries.
El código de las correspondientes teorías se encuentra aquí.