Zeros of the combination of the Eisenstein series for Γ0+(2)

Abstract

For even integers k≥ℓ≥4, we consider the modular forms Ek+Eℓ++Ek+ℓ+ for the Fricke group Γ0+(2), where Ek+ is the Eisenstein series of weight k for Γ0+(2), and we prove that if 26630≤ℓ<k≤77ℓ or k=ℓ≥10, then all of their zeros in the fundamental domain F+ for Γ0+(2) lie on the arc boundary of F+. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.