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# Continuity and value distribution of quantum modular forms

## January 31 at 16:00 – 17:00 CET

International Seminar on Automorphic Forms

Sandro Bettin (University of Genova)

Quantum modular forms are functions f defined on the rationals whose period functions, such as ψ(x):= f(x) – x^{-k} f(-1/x) (for level 1), satisfy some continuity properties. In the case of k=0, f can be interpreted as a Birkhoff sums associated with the Gauss map. In particular, under mild hypotheses on G, one can show convergence to a stable law. If k is non-zero, the situation is rather different and we can show that mild conditions on psi imply that f itself has to exhibit some continuity property. Finally, we discuss the convergence in distribution also in this case. This is a joint work with Sary Drappeau.

You can join the Zoom meeting at https://tu-darmstadt.zoom.us/j/68048280736

The password is the first Fourier coefficient of the modular j-function (as digits).