Banca de DEFESA: Diego Alves da Costa

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : Diego Alves da Costa
DATE: 30/10/2023
TIME: 14:00
LOCAL: videoconferência
TITLE:

On the problems B e C of Mahler

KEY WORDS:

Mahler's problems, one-dimensional transcendental functions,
multidimensional transcendental functions, exceptional sets, arithmetic behavior.

PAGES: 55
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

In this thesis work, we study two generalizations for problems proposed by Mahler in 1976 on the arithmetic behavior of analytic functions, namely, Problem B and Problem C. In the first generalization, we investigate the existence of entire and transcendental functions, with rational coefficients, such that both the image and the inverse image of the set of algebraic numbers by this function, and by all its derivatives, are subsets of $\bar{\mathbb{Q}}.$ In the second generalization, we characterize which subsets$\bar{\mathbb{Q}}^m,$ where $m$ is an integer number greater than or equal to $2,$ can be the exceptional set of an entire transcendental function $f: \C^m \rightarrow \C$ with rational coefficients.

COMMITTEE MEMBERS:
Externa à Instituição - ANA PAULA DE ARAUJO CHAVES - UFG
Interno - 1531891 - DIEGO MARQUES FERREIRA
Interno - 1122573 - HEMAR TEIXEIRA GODINHO
Interno - 404654 - NORAI ROMEU ROCCO
Externo à Instituição - VICTOR GONZALO LOPEZ NEUMANN - UFU