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Uniqueness of L-functions with weighted sharing | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 07 آذر 1403 اصل مقاله (376.98 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2024.31920.4735 | ||
| نویسندگان | ||
| Nasir Uddin Gazi1؛ Rana Mondal* 2 | ||
| 1Department of Mathematics and Statistics, Aliah University, IIA/27, AA II, Newtown, Kolkata-700160, India | ||
| 2Department of Mathematics, Cambridge Institute of Technology, Ranchi, 835103, Jharkhand, India | ||
| تاریخ دریافت: 05 مهر 1402، تاریخ پذیرش: 15 خرداد 1403 | ||
| چکیده | ||
| $L$-functions are complex functions associated with number-theoretic objects such as number fields, elliptic curves, modular forms, and automorphic representations. The general form of an $L$-function can be represented as a Dirichlet series, an Euler product, or in terms of its analytic continuation and functional equation. One of the most famous $L$-functions is the Riemann zeta function, defined as: $\zeta(s) = 1^{s} + 2^{-s} + 3^{-s} + \cdots = \sum_{n=1}^\infty n^{-s}$, where s is a complex number. $L$- function plays a fundamental role in studying prime numbers and connects to important conjectures like the Riemann Hypothesis. In this paper, we study the uniqueness of transcendental meromorphic functions and $L$-function whose certain difference-differential polynomials share a small function and rational function with weight, where $L$-function is a function that is Dirichlet series with the Riemann zeta function as the prototype. The Selberg class $S$ of $L$-functions is the set of all Dirichlet series $L(s)=\sum_{n=1}^{\infty}a(n)n^{-s}$ of a complex variable $s=\sigma + it$ with $ a(1) = 1$. | ||
| کلیدواژه‌ها | ||
| Uniqueness؛ Meromorphic functions؛ Entire functions؛ L-function؛ Sharing values | ||
| مراجع | ||
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[1] P.T.Y. Chern, On meromorphic functions with finite logarithmic order, Trans. Amer. Math. Soc. 358 (2006), no. 2, 473–489. [2] W.J. Hao and J.F. Chen, Uniqueness of L-functions concerning certain differential polynomials, Discrete Dyn. Nature Soc. 2018 (2018), no. 1, Article ID 4673165, 12 pages. [3] W.K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964. [4] I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193–206. [5] I. Lahiri and N. Mandal, Small functions and uniqueness of meromorphic functions, J. Math. Anal. Appl. 340 (2008), no. 2, 780—792. [6] I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin/New York, 1993. [7] F. Liu, X.M. Li, and H.X. Yi, Value distribution of L-functions concerning shared values and certain differential polynomials, Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 5, 41–46. [8] X.M. Li, F. Liu, and H.X. Yi, Results on L-functions of certain differential polynomials sharing one finite value, Filomat 33(2019), no. 18, 5767–5776. [9] B.Q. Li, A result on value distribution of L-functions, Proc. Amer. Math. Soc. 138 (2010), no. 6, 2071–2077. [10] N. Mandal and N.K. Datta, Uniqueness L-function and its certain differential monomial concerning small functions, J. Math. Comput. Sci. 10 (2020), no. 5, 2155–2163, [11] N. Mandal and N.K. Datta, Uniqueness of difference-differential polynomials of L-functions concerning weighted sharing, Int. J. Appl. Math. 34 (2021), no. 3, 471–483. [12] P. Sahoo, Meromorphic functions that share fixed points with finite weights, Bull. Math. Anal. 2 (2010), no. 4, 106–118 [13] A. Selberg, Old and new conjectures and results about a class of Dirichlet series, Proc. Amalfi Conf. Analytic Number Theory (Maiori, 1989), E. Bombieri et al. (eds.), Collected papers, Vol. II, Springer-Verlag, 1991, pp. 47–63. [14] J. Steuding, Value-Distribution of L-Functions, Lecture Notes in Mathematics, 1877, Springer, Berlin, 2007. [15] C.C. Yang and H.X. Yi, Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications, 557, Kluwer Academic Publishers Group, Dordrecht, 2003. [16] L. Yang, Value Distribution Theory, Springer-Verlag, Berlin Heidelberg, 1993. [17] J. Xu and X. Zhang, The zeros of q-shift difference polynomials of meromorphic functions, Adv. Differ. Equ. 2012 (2012), 1–10. | ||
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