On the zeros of Eisenstein series for Γ ∗ 0 (5) and Γ ∗ 0 (7)
Abstract
We locate almost all the zeros of the Eisenstein series associated with the Fricke groups of level 5 and 7 in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (1970). We also use the arguments of some terms of the Eisenstein series in order to improve existing error bounds.