Meromorphic Extensions of Dynamical Generating Functions and Applications to Schottky Groups

Abstract

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.

Date of Award	1 Aug 2013
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Mark Kambites (Supervisor) & Nigel Ray (Supervisor)