English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We study the spectral polynomial of the Treibich-Verdier potential. Suchspectral polynomial, which is a generalization of the classical Lamepolynomial, plays fundamental roles in both the finite-gap theory and the ODEtheory of Heun's equation. In this paper, we prove that all the roots of suchspectral polynomial are real and distinct under some assumptions. The proofuses the classical concept of Sturm sequence and isomonodromic theories. Wealso prove an analogous result for a polynomial associated with a generalizedLame equation. Differently, our new approach is based on the viewpoint of themonodromy data.

Real-root property of the spectral polynomial of the Treibich-Verdier potential and related problems