MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Does the functional equation of the Selberg Zeta function imply the Selberg trace formula?

BTW, the trace formula implies the functional equation.

share|cite|improve this question
Is that really ture ? – Chandan Singh Dalawat Oct 18 '12 at 4:14
I am sure it is ture. By taking some special test function in the trace formula we get the functional equation of the Selberg Zeta function. – 7-adic Oct 18 '12 at 5:37

No, you also need that there aren't too many zeros.

Then it works. I indicated the strategy here The Guinand-Weil explicit formula without entire function theory just in terms of the Riemann Zeta function.

Also there is a Lecture Notes in Mathematics by Jürgen Fischer (PhD thesis).

share|cite|improve this answer
Note the fact, that there aren't too many zeros can be read off from the functional equation in principle, since it together with the ''Euler product'' implies that the Selberg zeta function is of finite exponential order. – Marc Palm Oct 18 '12 at 11:04

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.