Math @ Duke

Publications [#302440] of Heekyoung Hahn
Papers Published
 Hahn, H, On zeros of Eisenstein series for genus zero Fuchsian groups,
Proceedings of the American Mathematical Society, vol. 135 no. 8
(August, 2007),
pp. 23912401, American Mathematical Society (AMS), ISSN 00029939 [doi]
(last updated on 2021/06/16)
Abstract: Let Γ ≤ SL (ℝ) be a genus zero Fuchsian group of the first kind with ∞ as a cusp, and let E 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 E 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 halfplane, and jΓ is the canonical hauptmodul for Γ. © 2007 American Mathematical Society Reverts to public domain 28 years from publication. 2 2k 2k Γ Gamma;


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