This thesis is concerned with finding meromorphic extensions to a half-plane containing zero for certain generating functions. In particular, we generalise a result due to Morita and use it to show that the zeta function associated to the geodesic flow over a quotient of a Schottky group can be meromorphically extended to a half-plane containing zero. Moreover, we show that the special value at zero can be calculated. These results are then generalised to obtain meromorphic extensions past zero for L-functions defined on quotients of Schottky groups and to provide an expression for the special value at zero. Finally we show that Morita's method can be adapted to provide a meromorphic extension to a half-plane containing zero for Poincaré series defined for a Schottky group, and that in special circumstances the value at zero can be calculated.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:568661 |
| Date | January 2013 |
| Creators | Mcmonagle, Aoife |
| Contributors | Ray, Nige; Kambites, Mark |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/meromorphic-extensions-of-dynamical-generating-functions-and-applications-to-schottky-groups(af657d7b-3b8a-4d14-8cff-c5258af3260c).html |
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