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In this paper, we first prove that the normality of a family of  k -valued algebroid functions is not equivalent to the normality of the family of the coefficient functions in general. Moreover, by combining the Valiron characteristic function of algebroid functions and the Schottky theorem of holomorphic functions, we investigate the growth relationship between the maximum modulus of an algebroid function and the maximum modulus of its coefficient functions. On this basis, we prove several normality criteria which do not need to restrict the quantity of branch points and contain a very interesting Montel-type normality criterion for entire algebroid function families.

The normality criteria for families of entire algebroid functions