Irrationality proofs for zeta values, moduli spaces and dinner parties

Francis Brown

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arXiv · 1412.6508

Irrationality proofs for zeta values, moduli spaces and dinner parties

Francis Brown

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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 Ap\'ery'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.

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Francis Brown. 2014-12-19. Irrationality proofs for zeta values, moduli spaces and dinner parties. https://arxiv.org/abs/1412.6508

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