21 citations · 40 across the 6 of their papers we have counts for
7 papers · 1 filter
Heun equation and Painlevé equation
Kouichi Takemura
We relate two parameter solutions of the sixth Painlevé equation and finite-gap solutions of the Heun equation by considering monodromy on a certain class of Fuchsian differential…
Fuchsian equation, Hermite-Krichever Ansatz and Painlevé equation
Kouichi Takemura
Several results on Heun's equation are generalized to a certain class of Fuchsian differential equations. Namely, we obtain integral representations of solutions and develop Hermit…
On eigenvalues of Lamé operator
Kouichi Takemura
We introduce two integral representations of monodromy on Lamé equation. By applying them, we obtain results on hyperelliptic-to-elliptic reduction integral formulae, finite-gap po…
The Heun equation and the Calogero-Moser-Sutherland system IV: the Hermite-Krichever Ansatz
Kouichi Takemura
We develop a theory for the Hermite-Krichever Ansatz on the Heun equation. As a byproduct, we find formulae which reduce hyperelliptic integrals to elliptic ones.
Analytic continuation of eigenvalues of the Lamé operator
Kouichi Takemura
Eigenvalues of the Lamé operator are studied as complex-analytic functions in period of an elliptic function. We investigate the branching of eigenvalues numerically and clarif…
The Heun equation and the Calogero-Moser-Sutherland system III: the finite gap property and the monodromy
Kouichi Takemura
A new approach to the finite-gap property for the Heun equation is constructed. The relationship between the finite-dimensional invariant space and the spectral curve is clarified.…