Research
My research interests are focused in Number Theory, more specifically in the following topics:
1. Transcendental Number Theory and Diophantine Approximation:
In 1932, Kurt Mahler presented a classification for transcendental numbers, dividing them into 3 classes: S-numbers, T-numbers and U-numbers. This latter class is sub-divided into infinite classes, the Um-numbers, which are transcendentals "well approximated" by algebraic numbers of degree m. We work with the purpose of finding explicit families ofUm-numbers, so that we can generate immediate examples in this class, as well as classifying famous mathematical constants (such as the pi number, which is still an open problem).
2. Diophantine Equations Related to Recurrent Sequences:
Our interest is in using Algebraic and Transcendent Numbers Theory techniques to find solutions to diophantine equations, especially exponential, related to linear recurrent sequences such as the Fibonacci sequence and its generalizations. It is also in our interest to verify the validity or otherwise of certain properties inherent in the Fibonacci sequence, for their generalizations, such as the k-bonacci sequence.
3. Double-Fibonacci Numbers:
Here we generalize the recurrence of the famous Fibonacci sequence, now for two variables, and we look for a relation of this new class of numbers, called Double-Fibonacci with the original sequence. We also studied a generalization of this double recurrence and found identities that relate these generalizations to Fibonacci numbers. In addition, we look for closed forms for the sum of Double-Fibonacci numbers and other identities.