Uniqueness of L-functions sharing finite sets with meromorphic functions having Deficient Poles
Nội dung chính của bài viết
Tóm tắt
In this paper we investigate the uniqueness of L-functions
sharing finite sets with meromorphic functions having deficient poles. As
a consequence, we have exhibited a extended version of a recent result of
A. Banerjee and A. Kundu [1]. The results obtained in this paper improve
and extend a recent result due to Khoai-An-Phuong [10] and a some result
in [18].
Chi tiết bài viết
Từ khóa
L-function, uniqueness, shared sets, Meromorphic function, Deficient Poles
Tài liệu tham khảo
[1] A. Banerjee and A. Kundu, On uniqueness of L-functions in terms of zeros of strong uniqueness polynomial, Cubo, A Mathematical Journal, Vol. 25, no. 03, pp. 497-514, 2023.
[2] A. A. Goldberg and I. V. Ostrovskii, Value Distribution of Meromorphic Functions, Translations of Mathematical Monographs, vol. 236, 2008.
[3] H. Fujimoto, On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math. 122, 2000, 1175-1203.
[4] H. Fujimoto, On uniqueness polynomials for meromorphic functions, Nagoya Math. J. 170, 2003, 33-46.
[5] W. K. Hayman, Meromorphic Functions, Clarendon, Oxford(1964).
[6] H. H. Khoai, V. H. An and N. X. Lai, Strong uniqueness polynomials of degree 6 and unique range sets for powers of meromorphic functions, Int. J. Math. (2018), Vol. 29, N. 5, pp. 122-140.
[7] H. H. Khoai, V. H. An, and L. Q. Ninh, Value-sharing and uniqueness for L-functions, Ann. Polon. Math., vol. 126, no. 3, pp. 265-278, 2021.
[8] H. H. Khoai and V. H. An, Determining an L-function in the extended Selberg class by its preimages of subsets, Ramanujan J., vol. 58, no. 1, pp. 253-267, 2022.
[9] H. H. Khoai, V. H. An, and N. D. Phuong, On value distribution of L-functions sharing finite sets with meromorphic functions, Bull. Math. Soc. Sci. Math. Roumanie, vol. 66(114), no. 3, pp. 265-280, 2023.
[10] P.-C. Hu and B. Q. Li, A simple proof and strengthening of a uniqueness theorem for L-functions, Canad. Math. Bull., 2016, 59, 119-122.
[11] B.Q. Li, A result on value distribution of L-functions, Proc. Amer. Math. Soc., Vol. 138, N. 6, 2010, 2071-2077.
[12] B.Q. Li, A uniqueness theorem for Dirichlet series satisfying a Riemann type functional equation,Adv. Math., 2011, 226, 4198-4211.
[13] P. Lin and W. Lin, Value distribution of L-functions concerning sharing sets, Filomat, 30:16 (2016), 3975-3806.
[14] J. Steuding, Value-Distribution of L-functions, Lecture Notes in Mathematics, 1877, Springer, 2007.
[15] C. C. Yang, H. X. Yi, Uniqueness theory of meromorphic functions, Kluwer Acad. Publ. (2003).
[16] A.-D. Wu and P.-C. Hu, Uniqueness theorems for Dirichlet series, Bull. Aust. Math. Soc. 91 (2015), 389-399.
[17] Q.-Q. Yuan, X.-M. Li, and H.-X. Yi, Value distribution of L-functions and uniqueness questions of F. Gross, Lith. Math. J., 58(2):249-262, 2018. Uniqueness of L-functions sharing finite sets ... 15
[18] J. L. Zhang and L. Z. Yang, Some results related to a conjecture of R.Br¨uck, J. Inequal. Pure Appl. Math. 8(1), Art. 18, 2007.
[2] A. A. Goldberg and I. V. Ostrovskii, Value Distribution of Meromorphic Functions, Translations of Mathematical Monographs, vol. 236, 2008.
[3] H. Fujimoto, On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math. 122, 2000, 1175-1203.
[4] H. Fujimoto, On uniqueness polynomials for meromorphic functions, Nagoya Math. J. 170, 2003, 33-46.
[5] W. K. Hayman, Meromorphic Functions, Clarendon, Oxford(1964).
[6] H. H. Khoai, V. H. An and N. X. Lai, Strong uniqueness polynomials of degree 6 and unique range sets for powers of meromorphic functions, Int. J. Math. (2018), Vol. 29, N. 5, pp. 122-140.
[7] H. H. Khoai, V. H. An, and L. Q. Ninh, Value-sharing and uniqueness for L-functions, Ann. Polon. Math., vol. 126, no. 3, pp. 265-278, 2021.
[8] H. H. Khoai and V. H. An, Determining an L-function in the extended Selberg class by its preimages of subsets, Ramanujan J., vol. 58, no. 1, pp. 253-267, 2022.
[9] H. H. Khoai, V. H. An, and N. D. Phuong, On value distribution of L-functions sharing finite sets with meromorphic functions, Bull. Math. Soc. Sci. Math. Roumanie, vol. 66(114), no. 3, pp. 265-280, 2023.
[10] P.-C. Hu and B. Q. Li, A simple proof and strengthening of a uniqueness theorem for L-functions, Canad. Math. Bull., 2016, 59, 119-122.
[11] B.Q. Li, A result on value distribution of L-functions, Proc. Amer. Math. Soc., Vol. 138, N. 6, 2010, 2071-2077.
[12] B.Q. Li, A uniqueness theorem for Dirichlet series satisfying a Riemann type functional equation,Adv. Math., 2011, 226, 4198-4211.
[13] P. Lin and W. Lin, Value distribution of L-functions concerning sharing sets, Filomat, 30:16 (2016), 3975-3806.
[14] J. Steuding, Value-Distribution of L-functions, Lecture Notes in Mathematics, 1877, Springer, 2007.
[15] C. C. Yang, H. X. Yi, Uniqueness theory of meromorphic functions, Kluwer Acad. Publ. (2003).
[16] A.-D. Wu and P.-C. Hu, Uniqueness theorems for Dirichlet series, Bull. Aust. Math. Soc. 91 (2015), 389-399.
[17] Q.-Q. Yuan, X.-M. Li, and H.-X. Yi, Value distribution of L-functions and uniqueness questions of F. Gross, Lith. Math. J., 58(2):249-262, 2018. Uniqueness of L-functions sharing finite sets ... 15
[18] J. L. Zhang and L. Z. Yang, Some results related to a conjecture of R.Br¨uck, J. Inequal. Pure Appl. Math. 8(1), Art. 18, 2007.