# What are the ramifications of Hamburger's characterisation of the zeta function?

I was thinking of this because the analogous characterisations of the gamma function are quite helpful, but I don't know of any applications of the zeta function charactersation.

-
It would be helpful if you make clear what Weil's result do you mean and what are "many complicated identities involving gamma functions". Please provide links or references. –  Wadim Zudilin May 12 '10 at 1:45
Wadim: He is referring to Weil's converse theorem. –  KConrad May 12 '10 at 2:14
Can the poster explain why he considers Weil's converse theorem and the Bohr--Mollerup theorem to be analogous? The Bohr--Mollerup theorem characterizes the Gamma function as the unique meromorphic functions satisfying a few conditions, but in Weil's theorem one purpose is to show that an $L$-function with a few properties comes from a known construction; usually you won't completely pin down the $L$-function on the nose by such a theorem (the space of solutions may not be one-dimensional). –  KConrad May 12 '10 at 2:44