The generalized Chebotarev problem in higher genus

2025/08/06 by Bertola, Marco
#Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2508.04661

Abstract

We consider the extension to higher genus Riemann surfaces of the classical Chebotarev problem, with a view towards the development of the theory of Padé approximants on algebraic curves. To this end we define an appropriate notion of capacity that mimics the standard one, following works of Chirka and of the author and collaborators. The nontrivial topology of the Riemann surface requires further specification of the ``homotopy class'' of the continua in the solution of the Chebotarev problem. We also discuss the relationship of this problem to the theory of Jenkins-Strebel quadratic differentials.

Citations

• Dirichlet energy and focusing NLS condensates of minimal intensity
• Chebotarov continua, Jenkins-Strebel differentials and related problems: a numerical approach
• Critical measures on higher genus Riemann surfaces
• Nonlinear steepest descent approach to orthogonality on elliptic curves
• Abelianization of Matrix Orthogonal Polynomials
• Padé approximants on Riemann surfaces and KP tau functions
• S-curves in Polynomial External Fields
• Orthogonal Polynomials and S-curves
• Critical measures, quadratic differentials, and weak limits of zeros of Stieltjes polynomials

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