ON THE ZEROS OF THE EISENSTEIN SERIES FOR Γ^*₀(5) AND Γ^*₀(7)

抄録

We locate almost all of 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 Rankin and Swinnerton-Dyer (On the zeros of Eisenstein series. Bull. London Math. Soc. 2 (1970), 169-170). We also use the arguments of some terms of the Eisenstein series in order to improve existing error bounds.