On the common zeros of quasi-modular forms for Γ₀⁺(N) of level N=1,2,3

2022/06/14 by Bo‐Hae Im, Hojin Kim, Im, Bo-Hae +3
Mathematics · #11F99 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary 11F11

paper · pdf · doi:10.48550/arxiv.2206.06798

openalex publication_date 2022/06/14 · openalex created_date 2022/06/17 · openalex updated_date 2026/07/28

Abstract

In this paper, we study common zeros of the iterated derivatives of the Eisenstein series for Γ₀⁺(N) of level N=1,2 and 3, which are quasi-modular forms. More precisely, we investigate the common zeros of quasi-modular forms, and prove that all the zeros of the iterated derivatives of the Eisenstein series \fracd^m E_k^(N)(τ)dτ^m of weight k=2,4,6 for Γ₀⁺(N) of level N=2,3 are simple by generalizaing the results of Meher \citeMEH and Gun and Oesterlé \citeSJ20 for SL₂(ℤ).

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