Does FE of Selberg Zeta function imply Trace formula? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T15:28:24Z http://mathoverflow.net/feeds/question/109972 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109972/does-fe-of-selberg-zeta-function-imply-trace-formula Does FE of Selberg Zeta function imply Trace formula? 7-adic 2012-10-18T03:39:19Z 2012-10-18T09:56:20Z <p>Does the functional equation of the Selberg Zeta function imply the Selberg trace formula?</p> <p>BTW, the trace formula implies the functional equation.</p> http://mathoverflow.net/questions/109972/does-fe-of-selberg-zeta-function-imply-trace-formula/109999#109999 Answer by Marc Palm for Does FE of Selberg Zeta function imply Trace formula? Marc Palm 2012-10-18T09:53:48Z 2012-10-18T09:53:48Z <p>No, you also need that there aren't too many zeros. </p> <p>Then it works. I indicated the strategy here <a href="http://mathoverflow.net/questions/62816/the-guinand-weil-explicit-formula-without-entire-function-theory/62836#62836" rel="nofollow">http://mathoverflow.net/questions/62816/the-guinand-weil-explicit-formula-without-entire-function-theory/62836#62836</a> just in terms of the Riemann Zeta function.</p> <p>Also there is a Lecture Notes in Mathematics by Jürgen Fischer (PhD thesis).</p>