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Banca de DEFESA: Marcelo Oliveira Ribeiro
Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.STUDENT : Marcelo Oliveira Ribeiro
DATE: 25/04/2023
TIME: 14:00
LOCAL: Departamento de Matemática
TITLE:
Some results on the transcendence of powers related to $U$- and $T$-numbers
KEY WORDS:
Transcendence, Powers, $U$-numbers, $T$-numbers.
PAGES: 52
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:
In this work we investigate the arithmetic nature of certain powers related to $U$-numbers and a subclass of $T$-numbers. The first two ensures, respectively, results in the transcendence of any algebraic number raised to a $U$-number and a generalization of the transcendence of the constant $e$ raised to a $U$-number. Still related to $U$-numbers, we get two other results: one which gives the transcendence of product between a non-zero algebraic and the constant $e,$ raised to a $U$-number, and another which tells us when numbers of the type $\alpha^{\ell}\cdot\beta^{\
ell^2},$ where $\alpha,\beta\in\QQ\setminus\{0,1\}$ and $\ell$ is the Liouville constant, are transcendentals.
We were able to prove two more results, which are technical, and give us only partial information. One of them ensures, for a subclass of $T$-numbers, which we call special $T$-numbers, the transcendence of all results that we prove to be valid for $U$-numbers. The other partially solves the open problem on the arithmetic nature of $\xi^{\xi},$ when $\xi$ is a Liouville number. We get such a result for a $G_{\delta}$ dense set of Liouville numbers, which we call $\epsilon$-strong Liouville numbers.
We were able to prove two more results, which are technical, and give us only partial information. One of them ensures, for a subclass of $T$-numbers, which we call special $T$-numbers, the transcendence of all results that we prove to be valid for $U$-numbers. The other partially solves the open problem on the arithmetic nature of $\xi^{\xi},$ when $\xi$ is a Liouville number. We get such a result for a $G_{\delta}$ dense set of Liouville numbers, which we call $\epsilon$-strong Liouville numbers.
BANKING MEMBERS:
Externa à Instituição - ANA PAULA DE ARAUJO CHAVES - UFG
Presidente - 1531891 - DIEGO MARQUES FERREIRA
Interno - 1122573 - HEMAR TEIXEIRA GODINHO
Externo ao Programa - 1275682 - MATHEUS BERNARDINI DE SOUZA
Externo à Instituição - VICTOR GONZALO LOPEZ NEUMANN - UFU
Notícia cadastrada em: 11/04/2023 11:00
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