On uniqueness of \(L\)-functions in terms of zeros of strong uniqueness polynomial
- Abhijit Banerjee abanerjeekal@gmail.com
- Arpita Kundu arpitakundu.math.ku@gmail.com
Downloads
DOI:
https://doi.org/10.56754/0719-0646.2503.497Abstract
In this article, we have mainly focused on the uniqueness problem of an \(L\)-function \(\mathcal{L}\) with an \(L\)-function or a meromorphic function \(f\) under the condition of sharing the sets, generated from the zero set of some strong uniqueness polynomials. We have introduced two new definitions, which extend two existing important definitions of URSM and UPM in the literature and the same have been used to prove one of our main results. As an application of the result, we have exhibited a much improved and extended version of a recent result of Khoai-An-Phuong [23]. Our remaining results are about the uniqueness of \(L\)-function under weighted sharing of sets generated from the zeros of a suitable strong uniqueness polynomial, which improve and extend some results in [12].
Keywords
Mathematics Subject Classification:
T. T. H. An, J. T.-Y. Wang, and P.-M. Wong, “Strong uniqueness polynomials: the complex case,” Complex Var. Theory Appl., vol. 49, no. 1, pp. 25–54, 2004, doi: 10.1080/02781070310001634601.
A. Banerjee and S. Maity, “Further investigations on a unique range set under weight 0 and 1,” Carpathian Math. Publ., vol. 14, no. 2, pp. 504–512, 2022.
A. Banerjee, “Uniqueness of meromorphic functions sharing two sets with finite weight II,” Tamkang J. Math., vol. 41, no. 4, pp. 379–392, 2010.
A. Banerjee and I. Lahiri, “A uniqueness polynomial generating a unique range set and vice versa,” Comput. Methods Funct. Theory, vol. 12, no. 2, pp. 527–539, 2012, doi: 10.1007/BF03321842.
A. Banerjee and S. Mallick, “On the characterisations of a new class of strong uniqueness polynomials generating unique range sets,” Comput. Methods Funct. Theory, vol. 17, no. 1, pp. 19–45, 2017, doi: 10.1007/s40315-016-0174-y.
H. Fujimoto, “On uniqueness of meromorphic functions sharing finite sets,” Amer. J. Math., vol. 122, no. 6, pp. 1175–1203, 2000.
H. Fujimoto, “On uniqueness polynomials for meromorphic functions,” Nagoya Math. J., vol. 170, pp. 33–46, 2003, doi: 10.1017/S0027763000008527.
F. Gross, “Factorization of meromorphic functions and some open problems,” in Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), ser. Lecture Notes in Math. Springer, Berlin-New York, 1977, vol. 599, pp. 51–67.
W. K. Hayman, Meromorphic functions, ser. Oxford Mathematical Monographs. Clarendon Press, Oxford, 1964.
P.-C. Hu and B. Q. Li, “A simple proof and strengthening of a uniqueness theorem for L- functions,” Canad. Math. Bull., vol. 59, no. 1, pp. 119–122, 2016, doi: 10.4153/CMB-2015- 045-1.
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, doi: 10.4064/ap201030-17-3.
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, doi: 10.1007/s11139- 021-00483-y.
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 (N.S.), vol. 66(114), no. 3, pp. 265–280, 2023.
I. Lahiri, “Weighted value sharing and uniqueness of meromorphic functions,” Complex Variables Theory Appl., vol. 46, no. 3, pp. 241–253, 2001, doi: 10.1080/17476930108815411.
P. Li and C.-C. Yang, “Some further results on the unique range sets of meromorphic functions,” Kodai Math. J., vol. 18, no. 3, pp. 437–450, 1995, doi: 10.2996/kmj/1138043482.
P. Lin and W. Lin, “Value distribution of L-functions concerning sharing sets,” Filomat, vol. 30, no. 14, pp. 3795–3806, 2016, doi: 10.2298/FIL1614795L.
A. Z. Mohon’ko, “The Nevanlinna characteristics of certain meromorphic functions,” Teor. Funkcii Funkcional. Anal. i Priložen., no. 14, pp. 83–87, 1971.
A. Selberg, “Old and new conjectures and results about a class of Dirichlet series,” in Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989). Univ. Salerno, Salerno, 1992, pp. 367–385.
J. Steuding, Value-distribution of L-functions, ser. Lecture Notes in Mathematics. Springer, Berlin, 2007, vol. 1877.
C.-C. Yang and H.-X. Yi, Uniqueness theory of meromorphic functions, ser. Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht, 2003, vol. 557, doi: 10.1007/978-94-017-3626-8.
H.-X. Yi, “The reduced unique range sets for entire or meromorphic functions,” Complex Variables Theory Appl., vol. 32, no. 3, pp. 191–198, 1997, doi: 10.1080/17476939708814990.
Q.-Q. Yuan, X.-M. Li, and H.-X. Yi, “Value distribution of L-functions and uniqueness questions of F. Gross,” Lith. Math. J., vol. 58, no. 2, pp. 249–262, 2018, doi: 10.1007/s10986-018- 9390-7.
- 09/106(0200)/2019-EMR-I
Most read articles by the same author(s)
- Abhijit Banerjee, Some uniqueness results on meromorphic functions sharing three sets II , CUBO, A Mathematical Journal: Vol. 13 No. 3 (2011): CUBO, A Mathematical Journal
Similar Articles
- Elena I. Kaikina, Leonardo Guardado-Zavala, Hector F. Ruiz-Paredes, S. Juarez Zirate, Korteweg-de Vries-Burgers equation on a segment , CUBO, A Mathematical Journal: Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal
- Abhijit Banerjee, Some uniqueness results on meromorphic functions sharing three sets II , CUBO, A Mathematical Journal: Vol. 13 No. 3 (2011): CUBO, A Mathematical Journal
- P. Jeyanthi, P. Nalayini, T. Noiri, Pre-regular \(sp\)-open sets in topological spaces , CUBO, A Mathematical Journal: Vol. 20 No. 1 (2018)
- Goutam Haldar, Uniqueness of entire functions whose difference polynomials share a polynomial with finite weight , CUBO, A Mathematical Journal: Vol. 24 No. 1 (2022)
- Indrajit Lahiri, Nintu Mandal, On a result of Q. Han, S. Mori and K. Tohge concerning uniquesness of meromorphic functions. , CUBO, A Mathematical Journal: Vol. 16 No. 1 (2014): CUBO, A Mathematical Journal
- Messaoud Bounkhel, Arc-wise Essentially Tangentially Regular Set-valued Mappings and their Applications to Nonconvex Sweeping Process , CUBO, A Mathematical Journal: Vol. 10 No. 1 (2008): CUBO, A Mathematical Journal
- José Sanabria, Edumer Acosta, Carlos Carpintero, Ennis Rosas, Continuity via ΛsI-open sets , CUBO, A Mathematical Journal: Vol. 17 No. 1 (2015): CUBO, A Mathematical Journal
- S. Richard, R. Tiedra de Aldecoa, Commutator criteria for strong mixing II. More general and simpler , CUBO, A Mathematical Journal: Vol. 21 No. 1 (2019)
- Renukadevi S. Dyavanal, Ashwini M. Hattikal, Madhura M. Mathai, Uniqueness of meromorphic functions sharing a set in annuli , CUBO, A Mathematical Journal: Vol. 18 No. 1 (2016): CUBO, A Mathematical Journal
- Tetsuo Furumochi, Periodic Solutions of Periodic Difference Equations by Schauder‘s Theorem , CUBO, A Mathematical Journal: Vol. 11 No. 3 (2009): CUBO, A Mathematical Journal
1 2 3 4 5 6 7 8 9 10 11 12 > >>
You may also start an advanced similarity search for this article.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 A. Banerjee et al.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.