(for pedagogical publication click here)

♦ Peer-reviewed articles 

Solving the membership problem for certain subgroups of ${\mathrm{SL}}_2(\mathbb{Z})$, with Sandie Han, Satyanand Singh, and Johann Thiel, Journal of Algebra 653 (2024), 281-297.

Rédei permutations with the same cycle structure, with Juliane Capaverde and Virgínia M. Rodrigues, Finite Fields and Their Applications 81 (2022), 102046.

A conjugate directions-type procedure for quadratic multiobjective optimization, with  Ellen H. Fukuda and Luis M. Graña Drummond, Optimization 71:2 (2022), 419-437.

Permutation binomials of the form $x^r(x^{q-1}+a)$ over ${\mathbb{F}}_{q^e}$, with Ivelisse Rubio and Javier Santiago, Finite Fields and Their Applications 79 (2022), 102003.

Rédei permutations with cycles of the same length, with Juliane Capaverde and Virgínia M. Rodrigues, Designs, Codes and Cryptography 88 (2020), 2561-2579.

Subgroups of $S{L}_2(\mathbb{Z})$ characterized by certain continued fraction representations, with Sandie Han, Satyanand Singh, and Johann Thiel, Proceedings of the American Mathematical Society 148 (2020), 3775–3786.

Maximal entries of elements in certain monoids, with Sandie Han, Satyanand Singh, and Johann Thiel, Integers 20 (2020), Paper No. A31, 35 pp.

Mean row values in ($u$,$v$)-Calkin-Wilf trees, with Sandie Han, Satyanand Singh, and Johann Thiel, In: Nathanson M. (eds) Combinatorial and Additive Number Theory III. CANT 2018. Springer Proceedings in Mathematics & Statistics, vol 297, 133–146 (2020).

Pure gaps on curves with many rational places, with Daniele Bartoli, Maria Montanucci, and Luciane Quoos, Finite Fields and Their Applications 53 (2018), 287–308.  

Orphans in forests of linear fractional transformations, with Sandie Han, Satyanand Singh, and Johann Thiel, The Electronic Journal of Combinatorics 23, 3, Paper 3.6 (2016), 24 pp.

One- and two-point codes over Kummer extensions, with Alonso S. Castellanos and Luciane Quoos, IEEE Transactions on Information Theory 62, 9 (2016), 4867–4872.

The ($u$,$v$)-Calkin-Wilf forest, with Sandie Han, Satyanand Singh, and Johann Thiel, International Journal of Number Theory 12, 5 (2016), 1311–1328.

Character theory of monoids over an arbitrary field, with Luciane Quoos and Benjamin Steinberg, Journal of Algebra 415 (2015), 107–126.

Permutation binomials over finite fields, with Michael E. Zieve, Transactions of the American Mathematical Society 361 (2009), 4169–4180.

Rational functions with linear relations, with Michael E. Zieve, Proceedings of the American Mathematical Society 136 (2008), 1403–1408.

Low complexity of normal elements over finite fields of characteristic two, with Lucia Moura, Daniel Panario, and David Thomson, IEEE Transactions on Computers 57, 7 (2008), 990–1001.

Sequences of consecutive smooth polynomials over a finite field, with Daniel Panario, Proceedings of the American Mathematical Society 135 (2007), 1271 – 1277.

Nonexistence of permutation binomials of certain shapes, with Michael E. Zieve, The Electronic Journal of Combinatorics 14, 1 (2007), N12.

The number of permutation binomials over ${\mathbb{F}}_{4p+1}$  where $p$ and $4p+1$ are primes, with Daniel Panario and Qiang Wang, The Electronic Journal of Combinatorics 13 (2006), R65.

 Solving systems of equations modulo pseudovarieties of abelian groups and hyperdecidability, with Manuel Delgado and Benjamin Steinberg, Proceedings of the International Conference on Semigroups and Languages, Lisbon, 2005.

♦ Books

Topics in Finite Fields with Applications to Cryptography and Coding Theory (in Portuguese), with Daniel Panario, IMPA Mathematical Publications, 26^th Brazilian Mathematics Colloquium, Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, 152 pages, 2007.

♦ Theses

Polynomials over Finite Fields: Relationships with Integers, and Permutation Polynomials, Ph.D. thesis, Carleton University, Canada, 2006.

Primality tests based on elliptic curves (in Portuguese), Master’s thesis, Universidade Federal Fluminense, Brazil, 1999.