**Birkhoff-James Inner functions and zero sets of analytic functions**

In this joint work with Javad Mashreghi and Raymond Cheng, I will discuss the notion of an inner function for Hilbert and Banach space of analytic functions and how this notion can be used, as was used by Beurling to discuss the Hardy space setting, to describe the zero sets of functions from these spaces. There will be a particular focus on the space l_{p}^{A}, the analytic functions whose power series coefficients belong to the sequence space l _{ p}.