For sufficiently large k and l, all zeros of E_k² + E_{2k}, E_k³ + E_{3k}, and E_k E_l + E_{k+l} in the fundamental domain lie on the arc A = {e^{iθ} : π/2 ≤ θ ≤ 2π/3}.
Hahn, On zeros of eisenstein series for genus zero fuchsian g roups, Pro- ceedings of the American Mathematical Society 135 (8) (2007) 239 1–2401
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Zeros of certain combinations of Eisenstein series of weight 2k, 3k, and k + l
For sufficiently large k and l, all zeros of E_k² + E_{2k}, E_k³ + E_{3k}, and E_k E_l + E_{k+l} in the fundamental domain lie on the arc A = {e^{iθ} : π/2 ≤ θ ≤ 2π/3}.