Algebraic periodic points of transcendental entire functions

2023/05/16 by Krumm, David, Marques, Diego, Moreira, Carlos Gustavo +1
#FOS: Mathematics #Number Theory (math.NT) #Primary 37P10 #Secondary 11Jxx

paper · doi:10.48550/arxiv.2305.09614

Abstract

We prove the existence of transcendental entire functions f having a property studied by Mahler, namely that f(ℚ)⊆ ℚ and f^-1(ℚ)⊆ ℚ, and in addition having a prescribed number of k-periodic algebraic orbits, for all k≥ 1. Under a suitable topology, such functions are shown to be dense in the set of all entire transcendental functions.

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