Orateur
Ryzsard Nest
(Univ. Copenhagen)
Description
The functional equation for the Riemann zeta function is based on analysis of asymptotic behaviour for t≈0 of expression like Tr$(\exp(-zD^2))$, where $D$ is, say, an elliptic operator on a smooth closed manifold $M$. In particular, it depends heavily on the the fact that the expressions like Tr$(\exp(-zD^2))$ have Melin transform which is holomorphic on a subspace of the complex plane of the form Re$(z)>C$, which is a consequence of finite dimensionality of $M$. We will construct an analogue of the meromorphic extension of the Riemann zeta function and prove the corresponding functional equation in the infinite dimensional limit case.
Author
Ryzsard Nest
(Univ. Copenhagen)
