Continuity and value distribution of quantum modular forms
Document Type
Lecture
Publication Date
2-21-2023
Abstract
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 sum associated with the Gauss map. In particular, under mild hypotheses on ψ, 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 ψ 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.
Relational Format
presentation
Recommended Citation
Bettin, Sandro, "Continuity and value distribution of quantum modular forms" (2023). Algebra/Number Theory Seminar. 7.
https://egrove.olemiss.edu/math_algebra_number_theory/7
