Automorphic Schwarzian equations

  title={Automorphic Schwarzian equations},
  author={Abdellah Sebbar and Hicham Saber},
  journal={Forum Mathematicum},
  pages={1621 - 1636}
Abstract This paper concerns the study of the Schwartz differential equation {h,τ}=s⁢E4⁡(τ){\{h,\tau\}=s\operatorname{E}_{4}(\tau)}, where E4{\operatorname{E}_{4}} is the weight 4 Eisenstein series and s is a complex parameter. In particular, we determine all the values of s for which the solutions h are modular functions for a finite index subgroup of SL2⁡(ℤ){\operatorname{SL}_{2}({\mathbb{Z}})}. We do so using the theory of equivariant functions on the complex upper-half plane as well as an… 
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