2024/03/08 by Khalil Besrour, Besrour, Khalil, Abdellah Sebbar +1 · 1 citation
Mathematics · Computer Science · #Algebraic and Geometric Analysis #Mathematics and Applications #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2403.04973
In this paper we study the modular differential equation y''+s E4 y=0 where E4 is the weight 4 Eisenstein series and s=π2r2 with r=n/m being a rational number in reduced form such that m≥ 7. This study is carried out by solving the associated Schwarzian equation \h,τ\=2 s E4 and using the theory of equivariant functions on the upper half-plane and the 2-dimensional vector-valued modular forms. The solutions are expressed in terms of the Gauss hypergeometric series. This completes the study of the above-mentioned modular differential equation of the associated Schwarzian equation given that the cases 1≤ m≤ 6 have already been treated in the litterature.