Abstract
Let $\unicode[STIX]{x1D70C}\in (0,\infty ]$ be a real number. In this short note, we extend a recent result of Marques and Ramirez [‘On exceptional sets: the solution of a problem posed by K. Mahler’, Bull. Aust. Math. Soc.94 (2016), 15–19] by proving that any subset of $\overline{\mathbb{Q}}\cap B(0,\unicode[STIX]{x1D70C})$, which is closed under complex conjugation and contains $0$, is the exceptional set of uncountably many analytic transcendental functions with rational coefficients and radius of convergence $\unicode[STIX]{x1D70C}$. This solves the question posed by K. Mahler completely.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
