On uniqueness of L-functions in terms of zeros of strong uniqueness polynomial

• Autores: Abhijit Banerjee, Arpita Kundu
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 25, Nº. 3, 2023, págs. 497-514
• Idioma: inglés
• DOI: 10.56754/0719-0646.2503.497
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen En este artículo nos hemos enfocado principalmente en el problema de unicidad de una L-función L con una L-función o una función meromorfa f bajo la condición de compartir los conjuntos, generados a partir del conjunto de ceros de algunos polinomios de unicidad fuerte. Hemos introducido dos definiciones nuevas, que extienden dos importantes definiciones existentes en la literatura de URSM y UPM, y las mismas han sido usadas para probar uno de nuestros resultados principales. Como una aplicación del resultado, exhibimos una versión mejorada y extendida de un resultado reciente de Khoai-An-Phuong [13]. Nuestros resultados restantes son sobre la unicidad de una L-función bajo la condición de compartir conjuntos pesados generados a partir de los ceros de un polinomio de unicidad fuerte apropiado, que mejora y extiende algunos resultados en [12].

  • English

    Abstract In this article, we have mainly focused on the uniqueness problem of an L-function 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 [13]. 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].

• Referencias bibliográficas
  • An, T. T. H.,Wang, J. T.-Y.,Wong, P.-M.. (2004). Strong uniqueness polynomials: the complex case. Complex Var. Theory Appl.. 49. 25-54
  • Banerjee, A.,Maity, S.. (2022). Further investigations on a unique range set under weight 0 and 1. Carpathian Math. Publ.. 14. 504
  • Banerjee, A.. (2010). Uniqueness of meromorphic functions sharing two sets with finite weight II. Tamkang J. Math.. 41. 379
  • Banerjee, A.,Lahiri, I.. (2012). A uniqueness polynomial generating a unique range set and vice versa. Comput. Methods Funct. Theory. 12....
  • Banerjee, A.,Mallick, S.. (2017). On the characterisations of a new class of strong uniqueness polynomials generating unique range sets. Comput....
  • Fujimoto, H.. (2000). On uniqueness of meromorphic functions sharing finite sets. Amer. J. Math.. 122. 1175
  • Fujimoto, H.. (2003). On uniqueness polynomials for meromorphic functions. Nagoya Math. J.. 170. 33-46
  • Gross, F.. (1977). Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976). Springer. Berlin-New York.
  • Hayman, W. K.. (1964). Meromorphic functions. Clarendon Press. Oxford.
  • Hu, P.-C.,Li, B. Q.. (2016). A simple proof and strengthening of a uniqueness theorem for L-functions. Canad. Math. Bull.. 59. 119
  • Khoai, H. H.,An, V. H.,Ninh, L. Q.. (2021). Value-sharing and uniqueness for L-functions. Ann. Polon. Math.. 126. 265
  • Khoai, H. H.,An, V. H.. (2022). Determining an L-function in the extended Selberg class by its preimages of subsets. Ramanujan J.. 58. 253
  • Khoai, H. H.,An, V. H.,Phuong, N. D.. (2023). On value distribution of L-functions sharing finite sets with meromorphic functions. Bull. Math....
  • Lahiri, I.. (2001). Weighted value sharing and uniqueness of meromorphic functions. Complex Variables Theory Appl.. 46. 241
  • Li, P.,Yang, C.-C.. (1995). Some further results on the unique range sets of meromorphic functions. Kodai Math. J.. 18. 437
  • Lin, P.,Lin, W.. (2016). Value distribution of L-functions concerning sharing sets. Filomat. 30. 3795
  • Mohon’ko, A. Z.. (1971). The Nevanlinna characteristics of certain meromorphic functions. Teor. Funkciĩ Funkcional. Anal. i Priložen.. 83
  • Selberg, A.. (1992). Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989). Univ. Salerno. Salerno.
  • Steuding, J.. (2007). Value-distribution of L-functions. Springer. Berlin.
  • Yang, C.-C.,Yi, H.-X.. (2003). Uniqueness theory of meromorphic functions. Kluwer Academic Publishers Group. Dordrecht.
  • Yi, H.-X.. (1997). The reduced unique range sets for entire or meromorphic functions. Complex Variables Theory Appl.. 32. 191
  • Yuan, Q.-Q.,Li, X.-M.,Yi, H.-X.. (2018). Value distribution of L-functions and uniqueness questions of F. Gross. Lith. Math. J.. 58. 249