Taussky-Todd Lecture

In my talk I will discuss global periods of an automorphic representation. The goal is to use these periods to construct global invariants of such representation. I will describe a procedure that in some cases allows to construct such global invariants using properties of appropriate $L$-functions. This procedure allows to give concise formulation of several known results relating periods with special values of $L$-functions. I will show an example when the value of such global invariant is given by an unusual Euler product (not of Langlands type).