Publications

Books

1. Algebra comutativa em quatro movimentos,  with Eduardo Tengan, Coleção Projeto Euclides-1st Edition 2015.

Papers-Preprints

1. R. Alvarenga, H. Borges,    On the number of elements with prescribed norm and trace. Pre-print. 

2. H. Borges, C. Gon\c calves Jr,  The p-rank of curves of  Fermat type.  arXiv preprint arXiv 2212.03987.

3. H. Borges, G. Korchmaros, P. Speziali,   Plane curves with a large linear automorphism group in characteristic p. arXiv preprint arXiv 2202.05765. 

4. H. Borges, J. A. Oliveira, F. E. Brochero Martınez,   On the number of rational points on Artin-Schreier hypersurfaces. Finite Fields and Their Applications,  90 (2023), 102229 

5. H. Borges, S. Fukasawa,  An elementary abelian p-cover of the Hermitian curve with many automorphisms, Mathematische Zeitschrift, 302, (2022)  695--706.

6. H. Borges, G. Duran,     Weierstrass pure gaps and codes on curves wit three distinguished points. IEEE Transactions on Information Theory}, 374, 68, (2022),  1-1.

7. H. Borges, M. Coutinho,    On the Zeta function and the automorphism group of the generalized Suzuki curve.  Transactions of the American Mathematical Society,  374, (2021),  1899--1917.

8. Borges, H., Reis, L, Minimal value set polynomials over fields of size p^3. To appear in Proceedings of the American Mathematical Society.

9. Borges, H.,Coutinho, M.,  On the Zeta function and the Automorphism Group of the Generalized Suzuki Curve. Transactions of the American Mathematical Society, v. 374, p. 1899-1917, 2021.

10. Bartoli, D. ; H. Borges  ; Quoos, L  . Rational functions with small value sets. Journal of Algebra, v. 565, p. 675-690, 2021. 

11. N. Arakelian, H. Borges, P. Speziali, The Hurwitz curve over a  finite  field    and its Weierstrass points for the morphism of lines. Finite Fields and Their Applications, v. 73, p. 101842, 2021.

12. Borges, H., Fukasawa, S. Galois Points for double-Frobenius Nonclassical      Curves.  Finite Fields and Their applications, v. 61, p. 101579, 2020. 

13. H. Borges, M. Coutinho, On some generalized Fermat curves and chords of an affinely regular polygon inscribed in a hyperbola. Journal of Pure and Applied Algebra 222 (2019) 239-249.

14. Miriam Abdon,  Herivelto   Borges, Luciane Quoos.  Weierstrass points on Kummer extensions. Advances in Geometry 19 (2019) 323-333.

15. N. Arakelian, H. Borges. Upper bounds for the number of rational points on curves over  Finite  Fields. Israel Journal of Mathematics 218 (2018), 177-199.

16. H. Borges, A. Sepúlveda, G. Tizziotti. Subcovers and codes on a class of trace-defining curves. IEEE Transactions on Information Theory (2018), 1-12.

17. H. Borges, G. Cook and  M. Coutinho. Plane sections of Fermat Surfaces over Finite Fields. Finite Fields and their Applications 52 (2018), p. 156-173. 

18. Herivelto Borges and Ricardo Conceicao. A new family of Castle and Frobenius nonclassical curves.  Journal of Pure and Applied Algebra 222 (2018) 994-1002.

19. H. Borges, M. Homma.  Points on singular Frobenius nonclassical curves. Bulletin of the Brazilian Mathematical Society 48 (2017) 93-101 

20. N. Arakelian, H. Borges. Frobenius nonclassicality of Fermat curves with respect to cubics. - Israel Journal of Mathematics 218 (2017) 273-297.

21. Herivelto Borges.  Frobenius nonclassical components of curves with separated variables.  Journal of Number Theory, v. 159, 402–426 (2016).

22. H. Borges, A. Sepúlveda, G. Tizziotti.  Weierstrass semigroup and Automorphism group of the curves Xn,r.  Finite Fields Appl. 36, 121–132 (2015).

23. N. Arakelian, H. Borges. Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree.   Acta Arithmetica, v.167, p.43-66, (2015).

24. Herivelto Borges , Fernado Torres and  Beatriz Motta. Complete Arcs arising from a generalization of the Hermitian Curve. Acta Arithmetica, v.164, p.101-118, (2014).

25. Herivelto Borges and Ricardo Conceicao. On the characterization of minimal value set polynomials. Journal of Number Theory 133 , no. 6, 2021– 2035 (2013).

26. Borges Filho, H. M. On multi-Frobenius nonclassical plane curves. Archiv der Mathematik  v. 93, p. 541-553, (2009).  

27. Borges H.  On complete (N, d)-arcs derived from plane curves. Finite Fields Appl. 15, 82–96 (2009).