On the zeros of Eisenstein series for $\mathbf{\Gamma_0^{*}(2)}$ and $\mathbf{\Gamma_0^{*}(3)}$
On the zeros of Eisenstein series for $\mathbf{\Gamma_0^{*}(2)}$ and $\mathbf{\Gamma_0^{*}(3)}$
We locate all of the zeros of the Eisenstein series associated with the Fricke groups $\Gamma_0^{*}(2)$ and $\Gamma_0^{*}(3)$ in their fundamental domains by applying and expanding the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (``{\it On the zeros of Eisenstein series}'', 1970).