整函数差分算子的唯一性
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摘要
利用复域差分方程的方法,研究差分多项式的唯一性问题,在某一个整函数具有正的亏值假设下,证明了2个不同整函数的差分算子CM分担某值时的唯一性问题,所得结果可以看作微分情形的差分模拟.
Under the assumption that a given entire equation has positive deficiency and with the method of complex difference equations,some results about the uniqueness of difference operators of finite order entire functions sharing values with the same multiplicities are presented. These findings can be seen as the difference analogue of differential cases.
Under the assumption that a given entire equation has positive deficiency and with the method of complex difference equations,some results about the uniqueness of difference operators of finite order entire functions sharing values with the same multiplicities are presented. These findings can be seen as the difference analogue of differential cases.
引文
[1] HAYMAN W K. Meromorphic functions[M]. Oxford:Clarendon Press,1964.
[2] YANG C C,YI H X. Uniqueness theory of meromorphic function[M]. Dordrecht:Kluwer Academic Publishers Group,2003.
[3] YI H X. A question of C.C.Yang on the uniqueness of entire functions[J]. Kodai Mathematical Journal,1990,13(1):39-46.
[4] CHIANG Y M,FEND S J. On the Nevanlinna characteristic of f(z+η)and difference equations in the complex plane[J]. Ramanujan Journal,2008,16(1):105-129.
[5] HALBURD R G,KORHONEN R J. Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations[J]. Journal of Mathematical Analysis Applications,2006,314(2):477-487.
[6] HALBURD R G,KORHONEN R J. Nevanlinna theory for the difference operator[J]. Annales AcademiScientiarum Fennnic:Mathematica,2006,31(2):463-478.
[7] BRCK R. On entire functions which share one value CM with their first derivate[J]. Results in Mathematics,1996,30(1/2):21-24.
[8] CHEN C X,CHEN Z X. A notes on entire functions and their differences[J]. Journal of Inequalities and Applications,2013,2013(587):1-17.
[9] CHEN Z X. On difference counterpart of Brück’s conjecture[J]. Acta Mathematica Scientia:Series B,2014,34(3):653-659.
[10] CHEN Z X,YI H X. On sharing values of meromorphic functions and their differences[J]. Results in Mathematics,2013,63(1/2):557-565.
[11] HUANG Z B,ZHANG R R. Uniqueness of the differences of meromorphic functions[J]. Analysis Mathematica,2018,44(4):461-473.
[12] LI X M,YI H X,KANG C Y. Notes on entire functions sharing an entire function of a smaller order with their difference operators[J]. Archiv der Mathematik,2012,99(3):261-270.
[13] LUO X D,LIN W C. Value sharing results for shifts of meromorphic functions[J]. Journal of Mathematical Analysis Applications,2011,377(2):441-449.
[14] CHARAK K S,KORHONEN R J,KUMAR G. A note on partial sharing of values of meromorphic functions with their shifts[J]. Journal of Mathematical Analysis Applications,2016,435(2):1241-1248.
[15]陈宗煊,黄志波.复域差分和差分方程的研究[J].华南师范大学学报(自然科学版),2013,45(6):26-33.CHEN Z X,HUANG Z B. Study on complex differences and difference equations[J]. Journal of South China Normal University(Natural Science Edition),2013,45(6):26-33.
[16] HEITTOKANGAS J,KORHONEN R,LAINE I,et al. Value sharing results for shifts of meromorphic functions,and sufficient condition for periodicity[J]. Journal of Mathematical Analysis Applications,2009,355(1):352-363.
[17] HEITTOKANGAS J,KORHONEN R,LAINE I,et al. Uniqueness of meromorphic functions sharing values with their shifts[J]. Complex Variables and Elliptic Equations,2011,56(1/2/3/4):81-92.
[18] HUANG Z B. Value distribution and uniqueness on qdifferences of meromorphic function[J]. Bulletin of Korean Mathematical Society,2013,50(4):1157-1171.
[19] ZHANG J J,LIAO L W. Entire functions sharing some values with their difference operators[J]. Science China Mathematics,2014,57(10):2143-2152.
[2] YANG C C,YI H X. Uniqueness theory of meromorphic function[M]. Dordrecht:Kluwer Academic Publishers Group,2003.
[3] YI H X. A question of C.C.Yang on the uniqueness of entire functions[J]. Kodai Mathematical Journal,1990,13(1):39-46.
[4] CHIANG Y M,FEND S J. On the Nevanlinna characteristic of f(z+η)and difference equations in the complex plane[J]. Ramanujan Journal,2008,16(1):105-129.
[5] HALBURD R G,KORHONEN R J. Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations[J]. Journal of Mathematical Analysis Applications,2006,314(2):477-487.
[6] HALBURD R G,KORHONEN R J. Nevanlinna theory for the difference operator[J]. Annales AcademiScientiarum Fennnic:Mathematica,2006,31(2):463-478.
[7] BRCK R. On entire functions which share one value CM with their first derivate[J]. Results in Mathematics,1996,30(1/2):21-24.
[8] CHEN C X,CHEN Z X. A notes on entire functions and their differences[J]. Journal of Inequalities and Applications,2013,2013(587):1-17.
[9] CHEN Z X. On difference counterpart of Brück’s conjecture[J]. Acta Mathematica Scientia:Series B,2014,34(3):653-659.
[10] CHEN Z X,YI H X. On sharing values of meromorphic functions and their differences[J]. Results in Mathematics,2013,63(1/2):557-565.
[11] HUANG Z B,ZHANG R R. Uniqueness of the differences of meromorphic functions[J]. Analysis Mathematica,2018,44(4):461-473.
[12] LI X M,YI H X,KANG C Y. Notes on entire functions sharing an entire function of a smaller order with their difference operators[J]. Archiv der Mathematik,2012,99(3):261-270.
[13] LUO X D,LIN W C. Value sharing results for shifts of meromorphic functions[J]. Journal of Mathematical Analysis Applications,2011,377(2):441-449.
[14] CHARAK K S,KORHONEN R J,KUMAR G. A note on partial sharing of values of meromorphic functions with their shifts[J]. Journal of Mathematical Analysis Applications,2016,435(2):1241-1248.
[15]陈宗煊,黄志波.复域差分和差分方程的研究[J].华南师范大学学报(自然科学版),2013,45(6):26-33.CHEN Z X,HUANG Z B. Study on complex differences and difference equations[J]. Journal of South China Normal University(Natural Science Edition),2013,45(6):26-33.
[16] HEITTOKANGAS J,KORHONEN R,LAINE I,et al. Value sharing results for shifts of meromorphic functions,and sufficient condition for periodicity[J]. Journal of Mathematical Analysis Applications,2009,355(1):352-363.
[17] HEITTOKANGAS J,KORHONEN R,LAINE I,et al. Uniqueness of meromorphic functions sharing values with their shifts[J]. Complex Variables and Elliptic Equations,2011,56(1/2/3/4):81-92.
[18] HUANG Z B. Value distribution and uniqueness on qdifferences of meromorphic function[J]. Bulletin of Korean Mathematical Society,2013,50(4):1157-1171.
[19] ZHANG J J,LIAO L W. Entire functions sharing some values with their difference operators[J]. Science China Mathematics,2014,57(10):2143-2152.