A question proposed by K. Mahler on exceptional sets of transcendental functions with integer coefficients: solution of a Mahler's problem

Diego Marques; Carlos Gustavo Moreira

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arXiv · 1708.09483

A question proposed by K. Mahler on exceptional sets of transcendental functions with integer coefficients: solution of a Mahler's problem

Diego Marques·Carlos Gustavo Moreira

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Abstract

In this paper, we shall prove that any subset of $\overline{\mathbb Q}\cap B(0,1)$, which is closed under complex conjugation and which contains the element $0$, is the exceptional set of uncountably many transcendental functions, analytic in the unit ball, with integer coefficients. This solves a strong version of an old question proposed by K. Mahler (1976).

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Diego Marques, Carlos Gustavo Moreira. 2017-08-30. A question proposed by K. Mahler on exceptional sets of transcendental functions with integer coefficients: solution of a Mahler's problem. https://arxiv.org/abs/1708.09483

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