The Chebyshev Property of Three Classes of Complete Hyperelliptic Integrals of the First Kind

• Tianrui An ^[1] ; Yanfei Dai ^[1] ; Zhiming Hu ^[2]
  1. [1] Zhejiang Normal University

     Zhejiang Normal University

     China

     
  2. [2] Shanghai University of Finance and Economics

     Shanghai University of Finance and Economics

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 4, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper investigates the Chebyshev property of three classes of complete hyperelliptic integrals of the first kind. Using recent advancements in the criterion function and employing some techniques and methods from symbolic computation, we prove that the three classes of complete hyperelliptic integrals are Chebyshev, and the exact bounds on the number of zeros of these Abelian integrals are one. Our results complement and enrich the existing results, and show that there exist other subfamilies of ovals of the hyperelliptic Hamiltonian which are not exceptional, but the corresponding complete hyperelliptic integrals of the first kind still satisfy the Chebyshev property.

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