An arithmetic holonomicity criterion and irrationality of the 2-adic period $\zeta_2(5)$

Abstract: I will present a new arithmetic criterion for a formal power series to satisfy a linear ODE on an affine curve over a global field. This result characterizes the holonomic functions by a sharp positivity condition on a suitably defined arithmetic degree for an adelic set where a given formal power series is analytic. As an application, based on Calegari's method with overconvergent p-adic modular forms, we derive an irrationality proof of the Leopoldt-Kubota 2-adic zeta value $\zeta_2(5)$. This is a joint work in progress with Frank Calegari and Yunqing Tang.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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