某些差分多项式的亏量

郑秀敏, 陈宗煊

数学学报 ›› 2011, Vol. 54 ›› Issue (6) : 983-992.

PDF(431 KB)
中国科学院数学与系统科学研究院期刊网
PDF(431 KB)
数学学报 ›› 2011, Vol. 54 ›› Issue (6) : 983-992. DOI: 10.12386/A2011sxxb0098
论文

某些差分多项式的亏量

    郑秀敏1, 陈宗煊2
作者信息 +

On Deficiencies of some Difference Polynomials

    Xiu Min ZHENG1, Zong Xuan CHEN2
Author information +
文章历史 +

摘要

Halburd和Korhonen指出研究复域差分的值分布问题对进一步研究复域差分与差分方程具有十分重要的意义. 本文得到了关于有限级亚纯函数的差分多项式的亏量的一些结果, 其中部分结果可视为微分多项式相应结果的差分模拟. 同时, 我们在一定条件下给出了经典的Valiron-Mohon'ko定理的一个差分模拟结果, 并且作为本文中的一个重要工具出现. 这些结果推广了前人已有结果.  

Abstract

Halburd and Korhonen posed that the study of the value distribution of complex differences plays an important role in the further study of complex differences and difference equations, which gained renewed interests recently. In this paper, we obtain some results on deficiencies of difference polynomials of meromorphic functions of finite order, some of which can be viewed as difference analogues of corresponding results of differential polynomials. And under some conditions, a difference analogue of the classical Valiron-Mohon’ko Theorem is also given as an important tool in this paper. These results improve previous findings.  

关键词

差分多项式 / 亚纯函数 / 有限级 / 亏量

Key words

Difference polynomial / meromorphic function / finite order / deficiency

引用本文

EndNote

Ris (Procite)

Bibtex

导出引用
郑秀敏, 陈宗煊. 某些差分多项式的亏量. 数学学报, 2011, 54(6): 983-992 https://doi.org/10.12386/A2011sxxb0098
Xiu Min ZHENG, Zong Xuan CHEN. On Deficiencies of some Difference Polynomials. Acta Mathematica Sinica, Chinese Series, 2011, 54(6): 983-992 https://doi.org/10.12386/A2011sxxb0098

参考文献

[1] Hayman W. K., Meromorphic Functions, Oxford: Clarendon Press, 1964.

[2] Laine I., Nevanlinna Theory and Complex Differential Equations, Berlin: Walter de Gruyter, 1993.

[3] Yang L., Value Distribution Theory, Berlin: Springer-Verlag; Beijing: Science Press, 1993.

[4] Bhoosnurmath S. S., Kulkarni M. N., Yu K. W., On the value distribution of differential polynomials, Bull. Korean Math. Soc., 2008, 45(3): 427-435.

[5] Clunie J., On a result of Hayman, J. London Math. Soc., 1967, 42: 389-392.

[6] Hayman W. K., Picard values of meromorphic functions and theire derivatives, Ann. Math., 1959, 70(1): 9-42.

[7] Milloux H., Les Fonctions Meromorphes et Leurs Deriv′ees, Paris: Hermann, 1940, 20.

[8] Yang C. C., On deficiencies of differential polynomials, Math. Z., 1970, 116: 197-204.

[9] Yang C. C., On deficiencies of differential polynomials II, Math. Z., 1972, 125: 107-112.

[10] Bergweiler W., Langley J. K., Zeros of differences of meromorphic functions, Math. Proc. Cambridge Philos. Soc., 2007, 142: 133-147.

[11] Chen B. Q., Chen Z. X., Li S., Properties on solutions of some q-difference equations, Acta Math. Sin. Ser. B, 2010, 26(10): 1877-1886.

[12] Chen Z. X., Huang Z. B., Zheng X. M., On properties of difference polynomials, Acta Math. Sci. Ser. B, 2011, 31: 627-633.

[13] Chen Z. X., Shon K. H., Estimates for the zeros of differences of meromorphic functions, Sci. China Ser. A, 2009, 52(11): 2447-2458.

[14] Chen Z. X., Shon K. H., Some results on difference Riccati equations, Acta Math. Sin. Ser. B, 2011, 27(6): 1091-1100.

[15] Chiang Y. M., Feng S. J., On the Nevanlinna characteristic of f(z + η) and difference equations in the complane plane, Ramanujan J., 2008, 16: 105-129.

[16] 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.

[17] Halburd R. G., Korhonen R. J., Finite-order meromorphic solutions and the discrete Painlev′e eqations, Proc. London Math. Soc., 2007, 94: 443-474.

[18] Halburd R. G., Korhonen R. J., Meromorphic solutions of difference equations, integrability and the discrete Painlev′e equations, J. Phys. A., 2007, 40: 1-38.

[19] Laine I., Yang C. C., Value distribution of difference polynomials, Proc. Japan Acad. Ser. A, 2007, 83: 148-151.

[20] Zhang J. L., Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl., 2010, 367: 401-408.

[21] Zheng X. M., Chen Z. X., Some properties of meromorphic solutions of q-difference equations, J. Math. Anal. Appl., 2010, 361: 472-480.

[22] Zheng X. M., Chen Z. X., On the value distribution of some difference polynomials, submitted.

[23] Mues E., Steinmetz N., The theorem of Tumura-Clunie for meromorphic functions, J. London Math. Soc., 1981, 23(2): 113-122.

基金

国家自然科学基金(10871076, 11026096);江西省教育厅青年科学基金(GJJ11072)

PDF(431 KB)

197

Accesses

0

Citation

Detail
段落导航
相关文章

/

〈 〉