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<p>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).</p>

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

  • 期刊论文

  • 发表日期：

    2025年10月13日

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  • Shaoqing Wang,
  • Yangjian Sun,
  • Guilin Ji

摘要

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).