On zeros of Eisenstein series for genus zero Fuchsian groups

Let Γ ≤ SL2(ℝ) be a genus zero Fuchsian group of the first kind with ∞ as a cusp, and let EΓ2k be the holomorphic Eisenstein series of weight 2k on Γ that is nonvanishing at ∞ and vanishes at all the other cusps (provided that such an Eisenstein series exists). Under certain assumptions on Γ, and on a choice of a fundamental domain F, we prove that all but possibly c(Γ, F) of the nontrivial zeros of EGamma;2k lie on a certain subset of {z ∈ h: jΓ(z) ∈ℝ}. Here c(Γ, F) is a constant that does not depend on the weight, h is the upper half-plane, and jΓ is the canonical hauptmodul for Γ. © 2007 American Mathematical Society Reverts to public domain 28 years from publication.

Duke Scholars

Author Heekyoung Hahn Mathematics