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On exceptional sets of transcendental functions with integer coefficients: solution of a problem of Mahler

Volume 192 / 2020

Diego Marques, Carlos Gustavo Moreira Acta Arithmetica 192 (2020), 313-327 MSC: Primary 11Jxx; Secondary 30Dxx. DOI: 10.4064/aa180326-13-2 Published online: 29 November 2019

Abstract

We prove that any subset of $\overline {\mathbb Q }\cap B(0,1)$ which is closed under complex conjugation and contains $0$ is the exceptional set of uncountably many transcendental functions, analytic in the unit ball, with integer coefficients. This strengthens a result of Mahler (1965) and answers a strong variant of an old question also proposed by Mahler (1976).

Authors

  • Diego MarquesDepartamento de Matemática
    Universidade de Brasília
    Brasília, DF, Brazil
    e-mail
  • Carlos Gustavo MoreiraInstituto de Matemática Pura e Aplicada
    Rio de Janeiro, RJ, Brazil
    e-mail

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