Meromorphic Extensions of Dynamical Generating Functions and Applications to Schottky Groups

  • Aoife Mcmonagle

Student thesis: Phd


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 Award1 Aug 2013
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorMark Kambites (Supervisor) & Nigel Ray (Supervisor)


  • L-function
  • zeta function
  • Schottky
  • PoincarĂ© series

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