Irrationality proofs for zeta values, moduli spaces and dinner parties

Abstract

A simple geometric construction on the moduli spaces ${\mathcal{M}}_{0,n}$ of curves of genus $0$ with $n$ ordered marked points is described which gives a common framework for many irrationality proofs for zeta values. This construction yields Apéry's approximations to $\zeta (2)$ and $\zeta (3)$, and for larger $n$, an infinite family of small linear forms in multiple zeta values with an interesting algebraic structure. It also contains a generalisation of the linear forms used by Ball and Rivoal to prove that infinitely many odd zeta values are irrational.

References in corpus (5)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Feynman integrals and hyperlogarithms
• Two hypergeometric tales and a new irrationality measure of $\zeta (2)$
• Deresonating a Tate period
• Formal weights in Kontsevich's formality construction and multiple zeta values