Zeta-functions in dimension 1 and 2 (continuation)

My first lecture was mostly concerned with the case of curves where I explained a version of the Tate-Iwasawa method and outlined how one can start to extend it to dimension 2. In the second lecture we will consider in details some pieces of this approach for surfaces. The exposition will be rather independent from the previous talk. Firstly, we give a survey of the representation theory for discrete finitely generated Heisenberg groups (moduli spaces of infinite-dimensional representations, characters as theta-functions, Mellin transform, Plancherel type Theorem). Next, we introduce adelic Heisenberg groups on surfaces and study their representation theory.