Diego Marques

Universidade de Brasília

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Pavel Trojovský

University of Hradec Králové

Carlos Gustavo Moreira

Instituto Nacional de Matemática Pura e Aplicada

Jean Lelis

Universidade Federal do Pará

Alain Togbé

Purdue University Northwest

Josimar Ramirez

Universidade de Brasília

Ana Paula Chaves

Universidade Federal de Goiás

Jonathan Sondow

New York Proton Center

Martı́n Mereb

Fundación Ciencias Exactas y Naturales

Jing-Jing Huang

University of Nevada, Reno

Dušan Bednařı́k

University of Hradec Králové

Cooperative Institutions

Universidade de Brasília

Universidade de São Paulo

Universidade Federal de Viçosa

Universidade Federal de Goiás

Institute of Astronomy and Space Physics

Hospital Universitário de Brasília

University of Hradec Králové

University of Buenos Aires

Universidade Federal de Mato Grosso do Sul

Czech Academy of Sciences, Institute of Mathematics

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Some Results on Arithmetic Properties of p-Adic Liouville Numbers

P-Adic Numbers Ultrametric Analysis and Applications (2019)

Jean Lelis Diego Marques

Ultrametric space

Real number

Transcendental function

10.1134/s207004661903004x

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Citations (1)

A NOTE ON LACUNARY POWER SERIES WITH RATIONAL COEFFICIENTS

Bulletin of the Australian Mathematical Society (2015)

Diego Marques Josimar Ramirez Elaine Silva

In this note, we prove that for any ${\it\nu}>0$ , there is no lacunary entire function $f(z)\in \mathbb{Q}[[z]]$ such that $f(\mathbb{Q})\subseteq \mathbb{Q}$ and $\text{den}f(p/q)\ll q^{{\it\nu}}$ , for all sufficiently large $q$ .

Lacunary function

10.1017/s0004972715001239

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Citations (4)

Some consequences of Schanuel's conjecture

Journal of Number Theory (2009)

Chuangxun Cheng Brian C. Dietel Mathilde Herblot Jing-Jing Huang Holly Krieger

10.1016/j.jnt.2008.10.018

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Citations (14)

On exceptional sets of transcendental functions with integer coefficients: solution of a problem of Mahler

Acta Arithmetica (2019)

Diego Marques Carlos Gustavo Moreira

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

Transcendental function

Transcendental equation

Ball (mathematics)

10.4064/aa180326-13-2

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Citations (3)

Fibonacci numbers at most one away from a product of factorials

Diego Marques

Let (Fn)n 0 be the Fibonacci sequence given byF0 = 0; F1 = 1 and Fn+2 = Fn+1 + Fn, forn 0. In this note, we find all solutions of the Diophantine equation

Sequence (biology)

Lucas number

Pisano period

Lucas sequence

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Transcendence Measures for some $U_m$-numbers related to Liouville's constant

arXiv (Cornell University) (2009)

Ana Paula Chaves Diego Marques

In this note, we shall prove that the sum and the product of an algebraic number $α$ by the \textit{Liouville constant} $L=\sum_{j=1}^{\infty}10^{-j!}$ is a $U$-number with type equals to the degree of $α$ (with respect to $\mathbb{Q}$). Moreover, we shall have that $\max\{w^{\ast}_n(αL),w^{\ast}_n(α+ L)\}\leq 2m^2n+m-1$, for $n=1,...,m-1$.

Transcendence (philosophy)

Constant (computer programming)

10.48550/arxiv.0910.3715

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Citations (0)

On Generalized Cullen and Woodall Numbers That are Also Fibonacci Numbers

J. Integer Seq. (2014)

Diego Marques

The m-th Cullen number Cm is a number of the form m2 m + 1 and the m-th Woodall number Wm has the form m2 m − 1. In 2003, Luca and Stuanicua proved that the largest Fibonacci number in the Cullen sequence is F4 = 3 and that F1 = F2 = 1 are the largest Fibonacci numbers in the Woodall sequence. A generalization of these sequences is defined by Cm,s = ms m +1 and Wm,s = ms m −1, for s > 1. In this paper, we search for Fibonacci numbers belonging to these generalized Cullen and Woodall sequences.

Sequence (biology)

Pisano period

Lucas number

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Citations (2)

On a class of transcendental entire functions mapping m-degree algebraic numbers into rational numbers

arXiv (Cornell University) (2014)

Diego Marques Josimar Ramirez

In this paper, we shall prove, for any $m\geq 1$, the existence of an uncountable subset of $U$-numbers of type $\leq m$ (which we called the set of {\it $m$-ultra numbers}) for which there exists uncountably many transcendental analytic functions mapping it into Liouville numbers.

Rational number

Transcendental function

Real number

Degree (music)

Algebraic extension

Cardinal number (linguistics)

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Citations (0)

The p-adic Order of Some Fibonomial Coefficients.

J. Integer Seq. (2015)

Diego Marques Pavel Trojovský

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Citations (6)

On the Arithmetic Behavior of Liouville Numbers under Rational Maps

arXiv (Cornell University) (2019)

Ana Paula Chaves Diego Marques Pavel Trojovsk ' y

In 1972, Alniacik proved that every strong Liouville number is mapped into the set of $U_m$-numbers, for any non-constant rational function with coefficients belonging to an $m$-degree number field. In this paper, we generalize this result by providing a larger class of Liouville numbers (which, in particular, contains the strong Liouville numbers) with this same property (this set is sharp is a certain sense).

Rational number

Constant (computer programming)

Real number

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Citations (1)