关于Nevanlinna方向存在性的一个证明.pdf

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1、学校代码：10663学号:4201310000358贵贵贵州州州师师师范范范大大大学学学硕硕硕士士士学学学位位位论论论文文文关关关于于于Nevanlinna方方方向向向存存存在在在性性性的的的一一一个个个证证证明明明AproofontheexistenceoftheNevanlinnadirection专业名称：基础数学专业代码：070101研究方向：函数论申请人姓名：沈艳导师姓名：伍鹏程(教授)二零一六年五月万方数据目录摘摘摘要要要········································································

2、···················IAbstract···························································································II1绪绪绪论论论································································································11.1国内外研究现状及研究意义···················································

3、·······11.2特征函数··················································································11.3Ahlfors-Shimizu特征···································································31.4Nevanlinna方向·········································································42Nevanlinna方方方向向

4、向存存存在在在性性性定定定理理理································································52.1吕以辇、张广厚证明方法·····························································52.2孙道椿证明方法·········································································73Nevanlinna方方方向向向存存存在在在性性性新新新的的的证证证明明明············

5、·············································144总总总结结结和和和展展展望望望······················································································19参参参考考考文文文献献献····························································································20附附附录录录····························

6、·······························································21致致致谢谢谢···························································································22原原原创创创性性性声声声明明明·························································································231万方数据摘要亚纯函数奇异方向的存在性问题

7、一直是幅角分布理论研究的一个非常有意义的课题。1983年，我国著名数学家吕以辇、张广厚首次给出了亚纯函数的Nevanlinna方向?0(?,?)?0(?,?)的定义并证明了在满足条件lim2=+∞和条件liminf=?<∞下，开平?→∞(log?)?→∞log?面

8、?

9、<+∞上的亚纯函数?(?)至少有一条Nevanlinna方向Δ(?)存在。1986年，孙道椿修改了方向亏值的定义，并重新定义了复平面上亚纯函数?0(?,?)的Nevanlinna方向。在lim2=+∞条件下证明了函数?(?)至少有一条Ne