Abstract: In this talk I will describe how to make sense of the function (1+t)^x over the integers. I will explain how different rings of analytic functions can be defined over the integers, and how this leads to global analytic geometry and global Hodge theory. If time permits I will also describe an analytic version of lambda-rings and how this can be used to define a cohomology theory for schemes over Z. This is joint work with Federico Bambozzi and Adam Topaz.