DOI QR코드

DOI QR Code

A NOTE ON UNICITY OF MEROMORPHIC FUNCTIONS IN SEVERAL VARIABLES

  • Yezhou Li (School of Science Beijing University of Posts and Telecommunications) ;
  • Heqing Sun (School of Science Beijing University of Posts and Telecommunications)
  • 투고 : 2022.09.18
  • 심사 : 2023.05.12
  • 발행 : 2023.07.01

초록

Let f(z) be a meromorphic function in several variables satisfying $$\lim_{r\rightarrow\infty}sup\frac{log T(r, f)}{r}=o.$$ We mainly investigate the uniqueness problem on f in ℂm sharing polynomial or periodic small function with its difference polynomials from a new perspective. Our main theorems can be seen as the improvement and extension of previous results.

키워드

과제정보

The authors want to express their thanks to the anonymous referees for their suggestions and valuable comments that improved the quality of the paper. We would also like to thank Professor Yu Tian for the helpful discussions.

참고문헌

  1. C. Berenstein, D.-C. Chang, and B. Q. Li, A note on Wronskians and linear dependence of entire functions in Cn, Complex Variables Theory Appl. 24 (1994), no. 1-2, 131-144. https://doi.org/10.1080/17476939408814706
  2. T.-B. Cao and L. Xu, Logarithmic difference lemma in several complex variables and partial difference equations, Ann. Mat. Pura Appl. (4) 199 (2020), no. 2, 767-794. https://doi.org/10.1007/s10231-019-00899-w
  3. Z. X. Chen, On the difference counterpart of Bruck's conjecture, Acta Math. Sci. Ser. B (Engl. Ed.) 34 (2014), no. 3, 653-659. https://doi.org/10.1016/S0252-9602(14)60037-0
  4. B. Q. Chen and S. Li, Uniqueness problems on entire functions that share a small function with their difference operators, Adv. Difference Equ. 2014 (2014), 311, 11 pp. https://doi.org/10.1186/1687-1847-2014-311
  5. Z. H. Chen and Q. Yan, Uniqueness problem of meromorphic functions sharing small functions, Proc. Amer. Math. Soc. 134 (2006), no. 10, 2895-2904. https://doi.org/10.1090/S0002-9939-06-08475-9
  6. B. M. Deng, D. Liu, Y. Gu, and M. Fang, Meromorphic functions that share a polynomial with their difference operators, Adv. Difference Equ. 2018 (2018), Paper No. 194, 15 pp. https://doi.org/10.1186/s13662-018-1645-4
  7. A. El Farissi, Z. Latreuch, B. Belaidi, and A. Asiri, Entire functions that share a small function with their difference operators, Electron. J. Differential Equations 2016 (2016), Paper No. 32, 13 pp.
  8. Z. Gao, R. Korhonen, J. Zhang, and Y. Zhang, Uniqueness of meromorphic functions sharing values with their nth order exact differences, Anal. Math. 45 (2019), no. 2, 321-334. https://doi.org/10.1007/s10476-018-0605-2
  9. P. C. Hu, P. Li, and C. C. Yang, Unicity of Meromorphic Mappings, Springer, New York, 2013.
  10. G. Jank, E. Mues, and L. Volkmann, Meromorphe Funktionen, die mit ihrer ersten und zweiten Ableitung einen endlichen Wert teilen, Complex Variables Theory Appl. 6 (1986), no. 1, 51-71. https://doi.org/10.1080/17476938608814158
  11. H. H. Kho'ai, V. H. An, and N. X. Lai, Value-sharing and uniqueness problems for nonArchimedean differential polynomials in several variables, Complex Var. Elliptic Equ. 63 (2018), no. 2, 233-249. https://doi.org/10.1080/17476933.2017.1300584
  12. B. Q. Li, Uniqueness of entire functions sharing four small functions, Amer. J. Math. 119 (1997), no. 4, 841-858. https://doi.org/10.1353/ajm.1997.0025
  13. P. Li, Entire functions that share one value with their linear differential polynomials, Kodai Math. J. 22 (1999), no. 3, 446-457. https://doi.org/10.2996/kmj/1138044096
  14. P. Li and C.-C. Yang, Uniqueness theorems on entire functions and their derivatives, J. Math. Anal. Appl. 253 (2001), no. 1, 50-57. https://doi.org/10.1006/jmaa.2000.7007
  15. Z. Liu and Q. C. Zhang, Difference uniqueness theorems on meromorphic functions in several variables, Turkish J. Math. 42 (2018), no. 5, 2481-2505. https://doi.org/10.3906/mat-1712-52
  16. R. Nevanlinna, Einige Eindeutigkeitssatze in der Theorie der Meromorphen Funktionen, Acta Math. 48 (1926), no. 3-4, 367-391. https://doi.org/10.1007/BF02565342
  17. M. Ru, Nevanlinna theory and its relation to Diophantine approximation, World Sci. Publishing, Inc., River Edge, NJ, 2001. https://doi.org/10.1142/9789812810519
  18. B. V. Shabat, Distribution of values of holomorphic mappings, translated from the Russian by J. R. King, translation edited by Lev J. Leifman, Translations of Mathematical Monographs, 61, Amer. Math. Soc., Providence, RI, 1985. https://doi.org/10.1090/mmono/061
  19. W. Wu and T.-B. Cao, Uniqueness theorems of meromorphic functions and their differences in several complex variables, Comput. Methods Funct. Theory 22 (2022), no. 2, 379-399. https://doi.org/10.1007/s40315-021-00389-2