Belyi functions of the special weighted trees of $(2,3)$-type

N. M. Adrianov, A. M. Vatuzov

Lomonosov Moscow State University

Abstract: 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.

UDC: 519.17+511.238