RATIONAL FUNCTIONS WITH TWO CRITICAL POINTS OF MAXIMUM MULTIPLICITY

摘要

In this paper, we consider the functions on algebraic curves whose divisors have the form nA - nC. Combinatorial-topological and algebraic descriptions are introduced for exploring such functions. All Belyi functions with such divisors are described. The case of curves of genus 1 is considered in more detail. The number of Belyi functions with divisor nA - nC is explicitly calculated. For general functions of this type on a curve of genus 1, we consider the space of the parameters and a method of its calculation that uses the Pade approximation.