97 citations · 579 across the 69 of their papers we have counts for
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Metrics with positive constant curvature and modular differential equations
Jia-Wei Guo, Chang-Shou Lin, Yifan Yang
In this paper, we consider the problem when a differential equation y"(z)=Q(z)y(z) is Fuchsian on H* and apparent on H, where Q(z) is a meromorphic modular form of weight 4 on SL(2…
On number and evenness of solutions of the Toda system on flat tori with non-critical parameters
Zhijie Chen, Chang-Shou Lin
We study the Toda system with singular sources \[ \begin{cases} Δu+2e^{u}-e^v=4π\sum_{k=0}^m n_{1,k}δ_{p_k}\quad\text{ on }\; E_τ,\\ Δv+2e^{v}-e^u=4π\sum_{k=0}^m n_{2,k}δ_{…
Modular Ordinary Differential Equations on of Third Order and Applications
Zhijie Chen, Chang-Shou Lin, Yifan Yang
In this paper, we study third-order modular ordinary differential equations (MODE for short) of the following form , $z\in\mathbb{H}=\{z\in\mathbb{C} \,|\,…
Proof of a conjecture of Dahmen and Beukers on counting integral Lamé equations with finite monodromy
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
In this paper, we prove Dahmen and Beukers' conjecture that the number of integral Lamé equations with index modulo scalar equivalence with the monodromy group dihedral …
Quasimodular forms and modular differential equations which are not apparent at cusps: I
Chang-Shou Lin, Yifan Yang
In this paper, we explore a two-way connection between quasimodular forms of depth and a class of second-order modular differential equations with regular singularities on the…