THE GROWTH OF p-ADIC ITERATED ENTIRE FUNCTIONS
By
Ratan Kumar Dutta
Department of Mathematics, Rishi Bankim Chandra College, Naihati, West Bengal, India- 743165
Email: ratan 3128@yahoo.com
(Received: December 20, 2023; In format : December 31, 2023; Revised : July 02, 2024; Accepted : July 30, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54213
Abstract
Let K be an algebraically closed p-adic complete field of characteristic 0 and A(K) be the K-algebra of entire functions on K. For any p -adic entire function f ∈ A(K) and r > 0, we denote |f|(r) the number sup {|f(x)| : |x| = r} where |.|(r) is a multiplicative norm on A(K). For f, g ∈ A(K), the ratio |f|(r) |g|(r) as r → ∞ is called growth of f with respect to g in terms of their multiplicative norm. In this paper, we define iteration of two function f, g ∈ A(K) and study the growth of p-adic iterated entire functions.
2020 Mathematical Sciences Classification: 30D35, 30G06, 46S10.
Keywords: Entire functions, Growth, Iteration, Order, Hyper order.