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<p>In this paper, we calculate the Belyi functions of the weighted trees of (2,&#xa0;3)-type with primitive special edge rotation groups. There are 21 Galois orbits of these trees: 6&#xa0;rational orbits, 12&#xa0;orbits over quadratic fields, and 3&#xa0;orbits over fields of degree 3, 4, and&#xa0;6. The highest degree of the calculated Belyi function is&#xa0;32. The calculations are performed using modular functions techniques.</p>

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BELYI FUNCTIONS OF THE SPECIAL WEIGHTED TREES OF \(\varvec{(2,3)}\)-TYPE

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • N. M. Adrianov,
  • A. M. Vatuzov

摘要

In this paper, we calculate the Belyi functions of the weighted trees of (2, 3)-type with primitive special edge rotation groups. There are 21 Galois orbits of these trees: 6 rational orbits, 12 orbits over quadratic fields, and 3 orbits over fields of degree 3, 4, and 6. The highest degree of the calculated Belyi function is 32. The calculations are performed using modular functions techniques.