涉及导数与差分的亚纯函数唯一性
Unicity of Meromorphic Functions Concerning Derivatives and Differences
设f,g是两个非常数亚纯函数,a是一个非零有穷复数,n ≥ 5是一个正整数.若[f(z)]n与[g(z)]n CM分担a,f(z)与g(z)CM分担∞,且N1)(r,f)=S(r,f),则或者f(z)≡ tg(z),其中tn=1;或者f(z)g(z)≡ t,其中tn=a2.由此改进了涉及导数与差分的一些亚纯函数唯一性的结果.
Let f, g be two nonconstant meromorphic functions, let a be a nonzero finite complex number, and let n ≥ 5 be a positive integer. If[f(z)]n and[g(z)]n share a CM, f(z) and g(z) share ∞ CM, and N1)(r, f)=S(r, f), then either f(z) ≡ tg(z), where tn=1, or f(z)g(z) ≡ t, where tn=a2. This improves some unicity results concerning derivatives and differences of meromorphic functions.
亚纯函数 / 导数 / 差分 / 唯一性 {{custom_keyword}} /
Meromorphic functions / derivatives / differences / unicity {{custom_keyword}} /
[1] Charak K. S., Korhonen R. J., Kumar G., A note on partial sharing of values of meromorphic functions with their shifts, J. Math. Anal. Appl., 2016, 435(2):1241-1248.
[2] Chen B. Q., Chen Z. X., Meromorphic function sharing two sets with its difference operator, Bull. Malays. Math. Sci. Soc., 2012, 35(3):765-774.
[3] Chen Z. X., On growth, zeros and poles of meromorphic solutions of linear and nonlinear difference equations, Sci. China Math., 2011, 54(10):2123-2133.
[4] Chiang Y. M., Feng S. J., On the Nevanlinna characteristic of f(z +η) and difference equations in the complex plane, Ramanujan J., 2008, 16:105-129.
[5] Chiang Y. M., Feng S. J., On the growth of logarithmic differences, difference quotients and logarithmic derivatives of meromorphic functions, Trans. Amer. Math. Soc., 2009, 361:3767-3791.
[6] Frank G., Eine Vermutung von Hayman über Nullstellen meromorpher Funktionen (in German), Math. Z., 1976, 149(1):29-36.
[7] Halburd R. G., Korhonen R. J., Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl., 2006, 314:477-487.
[8] Halburd R. G., Korhonen R. J., Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., 2006, 31:463-478.
[9] Hayman W. K., Meromorphic Functions, Clarendon Press, Oxford, 1964.
[10] Laine I., Yang C. C., Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc., 2007, 76(3):556-566.
[11] Liu K., Meromorphic functions sharing a set with applications to difference equations, J. Math. Anal. Appl., 2009, 359(1):384-393.
[12] Qi X. G., Li N., Yang L. Z., Uniqueness of meromorphic functions concerning their differences and solutions of difference Painleve equations, Comput. Methods Funct. Theory, 2018, 18:567-582.
[13] Yang L., Value Distribution Theory, Springer-Verlag, Berlin, 1993.
[14] Yi B., Li Y. H., Uniqueness of meromorphic functions that share two sets with CM (in Chinese), Acta Math. Sinica, 2012, 55(2):363-368.
[15] Yi H. X., Yang C. C., Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, 1995.
[16] Yi H. X., Meromorphic functions that share two sets (in Chinese), Acta Math. Sinica, 2002, 45(1):75-82.
[17] Zhang J. L., Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., 2010, 367(2):401-408.
[18] Zhang J., Liao L. W., Entire functions sharing some values with their difference operators, Sci. China Math., 2014, 57(10):2143-2152.
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