We develop a theory connecting the following three areas:(a) the mean field equation (MFE)
$\triangle u+ e^ u=\rho\,\delta_0 $, $\rho\in\mathbb R_ {> 0} $ on flat tori $ E_\tau=\mathbb …

Nous introduisons une forme pré-modulaire Z n (σ; τ) de poids 1 2 n (n+ 1) pour chaque n∈
ℕ, avec (σ, τ)∈ ℂ× ℍ, de sorte que pour E τ= ℂ/(ℤ+ ℤ τ), tout zéro non trivial de Z n (σ; τ) …

The behavior and the location of singular points of a solution to Painlevé VI equation could
encode important geometric properties. For example, Hitchin's formula indicates that …

We investigate the Liouvillian integrability of Hamiltonian systems describing a universe
filled with a scalar field (possibly complex). The tool used is the differential Galois group …

In this paper, we prove that the spectral curve Γ n of the generalized Lamé equation with the
Treibich–Verdier potential y ″(z)=[∑ k= 0 3 nk (n k+ 1)℘(z+ ω k 2| τ)+ B] y (z), nk∈ Z≥ 0 …

In this paper, the second in a series, we continue to study the generalized Lamé equation
with the Treibich-Verdier potential y ″(z)=[∑ k= 0 3 nk (n k+ 1)℘(z+ ω k 2| τ)+ B] y (z), nk∈ …

We study the singular $ SU (3) $ Toda system on a torus\[\begin {cases}\Delta u+ 2e^ ue^ v=
4\pi n\delta_0\\\Delta v+ 2e^ ve^ u= 4\pi n_2\delta_0\\\end {cases}\quad\textrm {on}\quad …

In this paper, the third in a series, we continue to study the generalized Lam\'{e} equation H
$(n_0, n_1, n_2, n_3; B) $ with the Darboux-Treibich-Verdier potential\begin {equation*} …

In this paper, we prove Dahmen and Beukers' conjecture that the number of integral Lam\'{e}
equations with index $ n $ modulo scalar equivalence with the monodromy group dihedral …

The Darboux-Treibich-Verdier (DTV) potential $\sum_ {k= 0}^{3} n_ {k}(n_ {k}+ 1)\wp
(z+\tfrac {\omega_ {k}}{2};\tau) $ is well-known as doubly-periodic solutions of the stationary …