On the zeros of Eisenstein series for $\mathbf{\Gamma_0^{*}(2)}$ and $\mathbf{\Gamma_0^{*}(3)}$

Abstract

We locate all of the zeros of the Eisenstein series associated with the Fricke groups ${\mathrm{\Gamma }}_0^{*}\left(2\right)$ and ${\mathrm{\Gamma }}_0^{*}\left(3\right)$ in their fundamental domains by applying and expanding the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer ("On the zeros of Eisenstein series", 1970).