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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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