Some results on asymptotic versions of Mahler's problems

2025/02/24 by Ricardo Francisco, Francisco, Ricardo, Diego Marques +1
Mathematics · #11J81 #30B10 #FOS: Mathematics #Number Theory (math.NT) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2502.17090

openalex publication_date 2025/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show the existence of a transcendental function f∈ℤ\z\ with coefficients that are almost all bounded such that f and all its derivatives assume algebraic values at algebraic points. Furthermore, we demonstrate that certain subsets of algebraic numbers are exceptional sets of some transcendental function f∈ℤ\z\ with almost all bounded coefficients.

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