3 citations · 8 across the 17 of their papers we have counts for
23 papers
Minimal Value Set Polynomials
Herivelto Borges, Lucas Reis
A well-known problem in the theory of polynomials over finite fields is the characterization of minimal value set polynomials (MVSPs) over the finite field , where $q…
Tate-Shafarevich results for quartic twists in characteristic
Herivelto Borges, João Paulo Guardieiro, Cecília Salgado +1
The aim of this paper is to present elliptic curves defined over function fields of even characteristic having arbitrarily large Mordell-Weil rank. More precisely, we study ellipti…
On the number of elements with prescribed norm and trace
Roberto Alvarenga, Herivelto Borges
Let F_q be the finite field with cardinality q, where q is a prime power. Given a finite field extension F_q^n over F_q and a,b in (F_q)^{*}, we investigate in this article the num…
The p-rank of curves of Fermat type
Herivelto Borges, Cirilo Gonçalves
Let be an algebraically closed field of characteristic . A pressing problem in the theory of algebraic curves is the determination of the -rank of a (nonsingul…
Plane curves with a large linear automorphism group in characteristic
H. Borges, G. Korchmáros, P. Speziali
Let be a subgroup of the three dimensional projective group defined over a finite field of order , viewed as a subgroup of $\mathrm{PGL}(3…
Weierstrass pure gaps on curves with three distinguished points
Herivelto Borges, Gregory Duran
Let be an algebraically closed field. In this paper, we consider the class of smooth plane curves of degree over , containing three points, $P_1,P_…