PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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


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).


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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image