Several Theorems of Algebroid Functions

TAN Yang

doi:10.6054/j.jscnun.2020015

Journal of South China Normal University (Natural Science Edition) > 2020 > 52(1): 100-103. > DOI: 10.6054/j.jscnun.2020015

TAN Yang. Several Theorems of Algebroid Functions[J]. Journal of South China Normal University (Natural Science Edition), 2020, 52(1): 100-103. DOI: 10.6054/j.jscnun.2020015

Citation:

TAN Yang. Several Theorems of Algebroid Functions[J]. Journal of South China Normal University (Natural Science Edition), 2020, 52(1): 100-103. DOI: 10.6054/j.jscnun.2020015

Citation:

TAN Yang. Several Theorems of Algebroid Functions[J]. Journal of South China Normal University (Natural Science Edition), 2020, 52(1): 100-103. DOI: 10.6054/j.jscnun.2020015

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Several Theorems of Algebroid Functions

TAN Yang^,

School of Applied Mathematics, Beijing Normal University, Zhuhai 519085, China

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Received Date: April 24, 2019
Available Online: March 21, 2021

Graphical Abstract

Abstract

Abstract

The Nevanlinna theory is used, firstly, to investigate the uniqueness of algebroid functions, extend the strengthening five-valued theorem of meromorphic function to algebroid function and obtain the strengthening 3v+1-valued theorem of algebroid function and, secondly, to study the relation between the characteristic functions of two algebroid functions when they share less shared values and extend the four-valued theorem of meromorphic function.
- algebroid function,
- uniqueness,
- characteristic function,
- shared value

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References (16)

References

[1]	何育赞.关于代数体函数的重值[J].数学学报, 1979, 22(6):733-742. http://d.old.wanfangdata.com.cn/Periodical/nysfxyxb201203001 HE Y Z. On the multiple values of algebroid functions[J]. Acta Mathematica Sinica, 1979, 22(6):733-742. http://d.old.wanfangdata.com.cn/Periodical/nysfxyxb201203001
[2]	何育赞.代数体函数与全纯函数线性组合的唯一性定理[J].纯粹数学与应用数学, 1985(1):24-31. HE Y Z. The uniqueness theorems of algebroid functions and linear combination of holomorphic functions[J]. Pure and Applied Mathematics, 1985(1):24-31.
[3]	姜云波, 高宗升.涉及CM分担值的代数体函数的唯一性[J].数学物理学报, 2014, 34A(4):796-801. http://d.old.wanfangdata.com.cn/Periodical/sxwlxb201404005 JIANG Y B, GAO Z S. Uniqueness of algebroid functions concerning CM shared values[J]. Acta Mathematica Scientia, 2014, 34A(4):796-801. http://d.old.wanfangdata.com.cn/Periodical/sxwlxb201404005
[4]	刘慧芳, 孙道椿.代数体函数与其导数的唯一性[J].数学物理学报, 2011, 31A(5):1296-1303. http://d.old.wanfangdata.com.cn/Periodical/sxwlxb201405025 LIU H F, SUN D C. On the uniqueness of algebroid functions and their derivatives[J]. Acta Mathematica Scientia, 2011, 31A(5):1296-1303. http://d.old.wanfangdata.com.cn/Periodical/sxwlxb201405025
[5]	孙道椿.代数体函数的增长性[J].华南师范大学学报(自然科学版), 2006(3):1-6. doi: 10.3969/j.issn.1000-5463.2006.03.001 SUN D C. On the growth of algebroid functions[J]. Journal of South China Normal University(Natural Science Edition), 2006(3):1-6. doi: 10.3969/j.issn.1000-5463.2006.03.001
[6]	孙道椿, 高宗升.代数体函数的唯一性定理[J].华南师范大学学报(自然科学版), 2005(3):80-85. doi: 10.3969/j.issn.1000-5463.2005.03.015 SUN D C, GAO Z S. Uniqueness theorems of algebroid functions[J]. Journal of South China Normal University(Natural Science Edition), 2005(3):80-85. doi: 10.3969/j.issn.1000-5463.2005.03.015
[7]	孙道椿, 高宗升.代数体函数的定理[J].数学学报, 2006, 49(5):1027-1032. doi: 10.3321/j.issn:0583-1431.2006.05.009 SUN D C, GAO Z S. On the theorems of algebroid functions[J]. Acta Mathematica Sinica, 2006, 49(5):1027-1032. doi: 10.3321/j.issn:0583-1431.2006.05.009
[8]	仪洪勋.关于代数体函数的重值与唯一性[J].工程数学学报, 1991, 8(4):1-8. YI H X. On the multiple values and uniqueness of algebroid functions[J]. Journal of Engineering Mathematics, 1991, 8(4):1-8.
[9]	张晓梅, 孙道椿, 柴富杰.有限级代数体函数的Borel方向[J].华南师范大学学报(自然科学版), 2019, 51(2):110-116. doi: 10.6054/j.jscnun.2019034 ZHANG X M, SUN D C, CHAI F J. Borel direction of finite order algebroid function[J]. Journal of South China Normal University(Natural Science Edition), 2019, 51(2):110-116. doi: 10.6054/j.jscnun.2019034
[10]	VALIRON G. Points de Picard et points de Borel des fonctions méromorphes dans un cercle[J]. Bulletin des Sciences Mathématiques, 1932, 56:10-32.
[11]	HE Y Z. Sur un problème d'unicite ralatif aux fonctions algébroídes[J]. Scientia Sinica, 1965, 14:174-180.
[12]	NEVANLINNA R. Le théorème de Picard-Borel et la théorie des fonctions méromorphes[M]. Paris: Gauthiers-Villars, 1929.
[13]	NEVANLINNA R. Einige eindeutigkeitssätze in der theorie der meromorphen funktionen[J]. Acta Mathematica, 1926, 48:367-391. doi: 10.1007/BF02565342
[14]	YANG C C, YI H X. Uniqueness theory of meromorphic function[M]. Dordrecht:Kluwer Press, 2003.
[15]	何育赞, 肖修治.代数体函数与常微分方程[M].北京:科学出版社, 1988.
[16]	孙道椿, 高宗升.代数体函数的值分布[M].北京:科学出版社, 2014.

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