Hampus Nyberg: Deep zero problems in the Bargmann-Fock space

The prevalence of analytic functions in mathematics may be attributed to both their generality but also their powerful uniqueness properties. A recently introduced class of uniqueness problems are deep zero problems where large amounts of information about analytic functions are given at a small number of points. We specialize to the Bargmann-Fock space consisting of entire functions which are square integrable with respect to the Gaussian measure. It's previously been shown that we have uniqueness in the case of two points, where the information is distributed equally in an arithmetic fashion. In this talk, we shall see how this may be extended to when the information is distributed 1 : 3 and also 1 : 4, again in an arithmetic fashion. This will rely on analysing some dynamical properties of irrational circle rotations.