On eigenvalues of Lamé operator

2004/09/15 by Kouichi Takemura, Takemura, Kouichi
Mathematics · Physics and Astronomy · #33E10 #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Nonlinear Waves and Solitons #math-ph #math.CA #math.MP #msc:33E10 #nlin.SI

paper · pdf · doi:10.48550/arxiv.math/0409247

13 pages, based on the talk given at the Workshop "Recent Progress in Solvable lattice Models" (Kyoto, July 2004)

arxiv created 2004/09/15 · openalex publication_date 2004/09/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 potential and eigenvalues of Lamé operator.

Citations

• Analytic continuation of eigenvalues of the Lamé operator

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