Mean field equations, hyperelliptic curves and modular forms. II

DOI10.5802/jep.51zbMath1376.33022arXiv1502.03295OpenAlexW3173349685MaRDI QIDQ2011992

Chin-Lung Wang, Chang-Shou Lin

Publication date: 27 July 2017

Published in: Journal de l'École Polytechnique -- Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.03295

zbMATH Keywords

Green's functionLamé equationLamé curveHeck functionHecke functionpre-modular formWeierstrass (elliptic) \(\wp\)-function

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Relationships between algebraic curves and integrable systems (14H70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Lamé, Mathieu, and spheroidal wave functions (33E10) Singular elliptic equations (35J75) Green's functions for elliptic equations (35J08)

Related Items (13)

Moduli spaces for Lamé functions and Abelian differentials of the second kind ⋮ Deformation of the spectrum for Darboux-Treibich-Verdier potential along \(\mathrm{Re}\,\tau =\frac{1}{2}\) ⋮ Moduli of spherical tori with one conical point ⋮ Elliptic KdV potentials and conical metrics of positive constant curvature. I ⋮ Exact number and non-degeneracy of critical points of multiple Green functions on rectangular tori ⋮ Spectrum of the Lamé operator and application. I: Deformation along \(\operatorname{Re} \tau = \frac{ 1}{ 2} \) ⋮ On the mean field type bubbling solutions for Chern-Simons-Higgs equation ⋮ A note on the critical points of the localization landscape ⋮ On algebro-geometric simply-periodic solutions of the KdV hierarchy ⋮ The geometry of generalized Lamé equation. I ⋮ Spectrum of the Lamé operator and application. II: When an endpoint is a cusp ⋮ The geometry of generalized Lamé equation. II: Existence of pre-modular forms and application ⋮ Even solutions of some mean field equations at non-critical parameters on a flat torus

Uses Software

• Mathematica

Cites Work

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• Mean field equations, hyperelliptic curves and modular forms. I
• Elliptic functions, Green functions and the mean field equations on tori
• Counting integral Lamé equations by means of dessins d’enfants
• Lamé polynomials, hyperelliptic reductions and Lamé band structure

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