On the zeros of certain Poincar\'e series for $\Gamma_0^*(2)$ and   $\Gamma_0^*(3)$
  We locate all of the zeros of certain Poincare series associated with the Fricke groups $\Gamma_0^*(2)$ and $\Gamma_0^*(3)$ in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (``On the zeros of Eisenstein series'', 1970). 
Junichi Shigezumi