On the Chebyshev Property of Degenerate Complete Hyperelliptic Integrals of the First Kind

• Shaoqing Wang ^[1] ; Yangjian Sun ^[2] ; Guilin Ji ^[3]
  1. [1] Central China Normal University

     Central China Normal University

     China

     
  2. [2] Shangrao Normal University

     Shangrao Normal University

     China

     
  3. [3] Guangxi Normal University

     Guangxi Normal University

     China

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 5, 2025
• Idioma: inglés
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• Resumen

  • This paper is devoted to the upper bound for the number of zeros of some classes of complete hyperelliptic integrals of the first kind. By some Chebyshev criterion of Abelian integrals, we obtain necessary and sufficient conditions for the integrals in degenerate cases to satisfy the Chebyshev property, which promotes the relevant work of research, including the work by Gavrilov and Iliev (2003), the one by N. Wang, J.

    Wang and D. Xiao (2013), as well as the one by C. Liu, Y. Sun and D. Xiao (2024).

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