Banca de DEFESA: Ricardo Francisco da Silva

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : Ricardo Francisco da Silva
DATE: 31/07/2023
TIME: 16:00
LOCAL: Departamento de Matemática
TITLE:

On Asymptotic Versions of the Problems A and C of Mahler

KEY WORDS:

Transcendental functions. Mahler’s problems. Exceptional sets. Asymptotic density.

PAGES: 63
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

The arithmetic nature of a number given as an image of an algebraic number by a transcendental function is a subject studied by several mathematicians since the 19th century. One of the main interested in this type of problem was Mahler, who proposed questions of great interest in Transcendental Number Theory. One of these questions deals
with the existence of a transcendental function with integer and bounded coefficients that assumes algebraic values at algebraic points. The first goal of this work is to show the existence of such a function, but with almost all bounded coefficients.

We will also show the existence of a transcendental function f ∈ Z{z} with almost all bounded coefficients such that f and all its derivatives take algebraic values in algebraic points.

Another problem proposed by Mahler asks whether there are transcendental functions with a prescribed exceptional set. Related to this problem, we show that certain subsets of algebraic numbers are exceptional sets of some transcendental function f ∈ Z{z} with almost all bounded coefficients.

COMMITTEE MEMBERS:
Externa à Instituição - ANA PAULA DE ARAUJO CHAVES - UFG
Presidente - 1531891 - DIEGO MARQUES FERREIRA
Interno - 1122573 - HEMAR TEIXEIRA GODINHO
Interno - 2518169 - KELLCIO OLIVEIRA ARAUJO
Externo à Instituição - VICTOR GONZALO LOPEZ NEUMANN - UFU