PDF(353 KB)
PDF(353 KB)
PDF(353 KB)
亚纯函数差分的亏量与值分布
The Deficiency and Value Distribution of Meromorphic Functions Concerning Difference
研究亚纯函数差分的亏量与值分布,证明了:设c是一个非零有穷复数,f(z)是复平面C上的超越整函数,n是一个正整数.若Δcnf(z)≠0,则或者f(z)取每个有穷复数无穷多次,或者Δcnf(z)取每个非零有穷复数无穷多次.
The paper studied the deficiency and value distribution of meromorphic functions concerning difference.We mainly proved:let c be a nonzero finite complex number,let f(z) be a transcendental entire function in C,and let n be a positive integer.If Δcnf(z)≠0,then either f(z) takes on every complex value infinitely often,or Δcnf(z) takes on every non-zero complex value infinitely often.
亚纯函数 / 亏量 / 值分布 / 差分 {{custom_keyword}} /
meromorphic function / deficiency / value distribution / difference {{custom_keyword}} /
[1] Bergweiler W., Langley J. K., Zeros of differences of meromorphic functions, Math. Proc. Cambridge Philos. Soc., 2007, 142:133-147.
[2] 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.
[3] Chen Z. X., Relationships between entire functions and their forward differences, Complex Var. Elliptic Equ., 2013, 58:299-307.
[4] Chen Z. X., Shon K. H., Estimates for the zeros of differences of meromorphic functions, Sci. China Ser. A, 2009, 52:2447-2458.
[5] 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.
[6] Chiang Y. M., Feng S. J., On the growth of logarithmic differences, difference quotients and logatithmic derivatives of meromorphic functions, Trans. Amer. Math. Soc., 2009, 361:3767-3791.
[7] Drasin D., The inverse problem of the Nevanlinna theory, Acta Math., 1976, 138(1-2):83-151.
[8] 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.
[9] Halburd R. G., Korhonen R. J., Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math., 2006, 31:463-478.
[10] Halburd R. G., Korhonen R. J., Finite order meromorphic solutions and the discrete Painlevé equations, Proc. Lond. Math. Soc., 2007, 94(3):443-474.
[11] Hayman W. K., Meromorphic Functions, Clarendon Press, Oxford, 1964.
[12] Laine I., Yang C. C., Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc., 2007, 76(2):556-566.
[13] Langley J. K., Value distribution of differences of meromorphic functions, Rocky Mountain J. Math., 2011, 41:275-291.
[14] Lan S. T., Chen Z. X., Relationships between characteristic functions of Δnf and f, J. Math. Anal. Appl., 2014, 412:922-942.
[15] Lan S. T., Chen Z. X., On value distribution of Δnf, Acta Math. Sin. Engl. Ser., 2014, 30(10):1795-1809.
[16] Pfluger A., Zur defektrelation ganzer funktionen endlicher ordnung (German), Comment. Math. Helv., 1946, 19:91-104.
[17] Yang L., Value Distribution Theory, Springer-Verlag, Berlin, 1993.
[18] Yang C. C., Yi H. X., Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers Group, Dordrecht, 2003.
[19] Yi H. X., Some theorems on systems of meromorphic functions (in Chinese), Shandong Daxue Xuebao Ziran Kexue Ban, 1997, 32(2):121-127.
[20] Zhang R. R., Chen Z. X., Value distribution of difference polynomials of meromorphic functions (in Chinese), Sci. Sin. Math., 2012, 42(11):1115-1130.
[21] Zhang R. R., Chen Z. X., Value distribution of meromorphic functions and their differences, Turk. J. Math., 2012, 36:395-406.
国家自然科学基金资助项目(11371149)
/
| 〈 |
|
〉 |
