亚纯函数的超越方向和Borel方向

Transcendental Directions and Borel Directions of Meromorphic Functions

利用Nevanlinna理论研究了亚纯函数的Borel方向和超越方向之间的关系以及函数与其导数的公共超越方向.当亚纯函数具有正增长级时,其Borel方向必然是该函数的超越方向.对于有穷正级ρ的整函数,含有Borel方向的超越方向集合分支的Lebesgue测度至少为min{2π,π/ρ},且其导数的超越方向必然也是该函数的超越方向.

The relation between transcendental directions and Borel directions of meromorphic functions is studied by using Nevanlinna theory.For meromorphic functions of positive order,the Borel directions must be the transcendental directions.Especially,for entire function f with positive orderρ,the component of the set of transcendental directions with a Borel direction has Lebesgue measure no less than min{2π,π/ρ},and every transcendental direction of f′ must be the transcendental direction of f.