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Title: Meromorphic extensions of dynamical generating functions and applications to Schottky groups
Author: Mcmonagle, Aoife
ISNI:       0000 0004 2737 7377
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2013
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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.
Supervisor: Ray, Nige; Kambites, Mark Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: zeta function ; Schottky ; L-function ; Poincaré series