A New Interpretation of the Selberg Trace Formula

Cartier, P.; Voros, A.

dc.contributor.author	Cartier, P.	en
dc.contributor.author	Voros, A.	en
dc.date.accessioned	2009-08-28T03:22:30Z	en
dc.date.available	2009-08-28T03:22:30Z	en
dc.date.issued	2004	en
dc.identifier.citation	Department of Mathematics - Research Reports-520 (2004)	en
dc.identifier.issn	1173-0889	en
dc.identifier.uri	http://hdl.handle.net/2292/5104	en
dc.description.abstract	We extend the Selberg trace formula for a hyperbolic compact Riemann surface to some new test functions, i.e., holomorphic and decreasing at infinity in a sector instead of a horizontal strip (and no longer even). As applications: 1) we interpret the trace formula as a Poisson summation formula involving the eigenvalue spectrum of the hyperbolic Laplacian on one side, and the lengths of all (real and complex) periodic geodesics of the surface on the other side; 2) we obtain a closed meromorphic continuation formula for a spectral zeta function of the hyperbolic Laplacian.	en
dc.publisher	Department of Mathematics, The University of Auckland, New Zealand	en
dc.relation.ispartofseries	Research Reports - Department of Mathematics	en
dc.rights.uri	https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm	en
dc.source.uri	http://www.math.auckland.ac.nz/Research/Reports/view.php?id=520	en
dc.title	A New Interpretation of the Selberg Trace Formula	en
dc.type	Technical Report	en
dc.subject.marsden	Fields of Research::230000 Mathematical Sciences::230100 Mathematics	en
dc.rights.holder	The author(s)	en