Irrationality proofs for zeta values, moduli spaces and dinner parties.(English)Zbl 1370.11103

Summary: A simple geometric construction on the moduli spacesordered 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 K. Ball and T. Rivoal [Invent. Math. 146, No. 1, 193–207 (2001; Zbl 1058.11051)] to prove that infinitely many odd zeta values are irrational.

MSC:

 11M32 Multiple Dirichlet series and zeta functions and multizeta values 11J82 Measures of irrationality and of transcendence 14H15 Families, moduli of curves (analytic) 32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)

Zbl 1058.11051
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