On unique range sets of meromorphic functions in ℂ m

Xiao-Tian Bai; Qi Han

Archivum Mathematicum (2007)

  • Volume: 043, Issue: 3, page 185-195
  • ISSN: 0044-8753

Abstract

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By considering a question proposed by F. Gross concerning unique range sets of entire functions in ℂ , we study the unicity of meromorphic functions in ℂ m that share three distinct finite sets CM and obtain some results which reduce 5 ≤ c 3 ( ℳ ( ℂ m ) ) ≤ 9 to 5 ≤ c 3 ( ℳ ( ℂ m ) ) ≤ 6 .

How to cite

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Bai, Xiao-Tian, and Han, Qi. "On unique range sets of meromorphic functions in $\mathbb {C}^m$." Archivum Mathematicum 043.3 (2007): 185-195. <http://eudml.org/doc/250158>.

@article{Bai2007,
abstract = {By considering a question proposed by F. Gross concerning unique range sets of entire functions in $\mathbb \{C\}$, we study the unicity of meromorphic functions in $\mathbb \{C\}^m$ that share three distinct finite sets CM and obtain some results which reduce $5\le c_3(\mathcal \{M\}(\mathbb \{C\}^m))\le 9$ to $5\le c_3(\mathcal \{M\}(\mathbb \{C\}^m))\le 6$.},
author = {Bai, Xiao-Tian, Han, Qi},
journal = {Archivum Mathematicum},
keywords = {entire (holomorphic) functions; meromorphic functions; unique range sets; linearly (in)dependent; entire (holomorphic) functions; meromorphic functions; unique range sets; linearly (in)dependent},
language = {eng},
number = {3},
pages = {185-195},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On unique range sets of meromorphic functions in $\mathbb \{C\}^m$},
url = {http://eudml.org/doc/250158},
volume = {043},
year = {2007},
}

TY - JOUR
AU - Bai, Xiao-Tian
AU - Han, Qi
TI - On unique range sets of meromorphic functions in $\mathbb {C}^m$
JO - Archivum Mathematicum
PY - 2007
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 043
IS - 3
SP - 185
EP - 195
AB - By considering a question proposed by F. Gross concerning unique range sets of entire functions in $\mathbb {C}$, we study the unicity of meromorphic functions in $\mathbb {C}^m$ that share three distinct finite sets CM and obtain some results which reduce $5\le c_3(\mathcal {M}(\mathbb {C}^m))\le 9$ to $5\le c_3(\mathcal {M}(\mathbb {C}^m))\le 6$.
LA - eng
KW - entire (holomorphic) functions; meromorphic functions; unique range sets; linearly (in)dependent; entire (holomorphic) functions; meromorphic functions; unique range sets; linearly (in)dependent
UR - http://eudml.org/doc/250158
ER -

References

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  5. Gross F., On the distribution of values of meromorphic functionas, Trans. Amer. Math. Soc. 131 (1968), 199–214. (1968) MR0220938
  6. Gross F., Factorization of meromorphic functions and some open problems, Complex Analysis (Proc. Conf. Univ. Kentucky, Lexington, Kentucky, 1976), Lecture Notes in Math. 599, Springer, Berlin, 1977. (1976) MR0450529
  7. Hayman W. K., Meromorphic Functions, Clarendon Press, Oxford, 1964. (1964) Zbl0115.06203MR0164038
  8. Hu P. C., Li C., Yang C. C., Unicity of Meromorphic Mappings, Kluwer Academic, Dordrecht, 2003. Zbl1074.30002MR1988768
  9. Jin L., Ru M., A unicity theorem for moving targets counting multiplicities, Tôhoku Math. J. 57 (2005), 589–595. Zbl1106.32017MR2203548
  10. Vitter A., The lemma of the logarithmic derivative in several complex variables, Duke Math. J. 44 (1977), 89–104. (1977) Zbl0361.32003MR0432924
  11. Yang C. C., Yi H. X., Uniqueness Theory of Meromorphic Functions, Science Press & Kluwer Academic, Beijing & Dordrecht, 2003. Zbl1070.30011MR2105668
  12. Yi H. X., On a question of Gross concerning uniqueness of entire functions, Bull. Austral. Math. Soc. 57 (1998), 343–349. (1998) Zbl0905.30026MR1617332

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