Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Herivelto Borges"'
Publikováno v:
Finite Fields and Their Applications. 90:102229
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::59d81593445e2e07ea318b0e33ba3425
https://doi.org/10.1016/j.ffa.2023.102229
https://doi.org/10.1016/j.ffa.2023.102229
Autor:
Herivelto Borges, Lucas Reis
Publikováno v:
Proceedings of the American Mathematical Society. 149:3639-3649
For any prime number p p , and integer k ⩾ 1 k\geqslant 1 , let F p k \mathbb {F}_{p^k} be the finite field of p k p^k elements. A famous problem in the theory of polynomials over finite fields is the characterization of all nonconstant polynomials
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cb672cf02d828889b0ba04e594a1cc56
https://doi.org/10.1090/proc/15478
https://doi.org/10.1090/proc/15478
Autor:
Mariana Coutinho, Herivelto Borges
Publikováno v:
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP
Universidade de São Paulo (USP)
instacron:USP
For p p an odd prime number, q 0 = p t q_{0}=p^{t} , and q = p 2 t − 1 q=p^{2t-1} , let X G S \mathcal {X}_{\mathcal {G}_{\mathcal {S}}} be the nonsingular model of Y q − Y = X q 0 ( X q − X ) . \begin{equation*} Y^{q}-Y=X^{q_{0}}(X^{q}-X). \en
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::61853279e7fedee389aac355b40f169c
https://doi.org/10.1090/tran/8286
https://doi.org/10.1090/tran/8286
Autor:
Herivelto Borges, Satoru Fukasawa
Publikováno v:
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP
Universidade de São Paulo (USP)
instacron:USP
The full automorphism group of a certain elementary abelian $p$-cover of the Hermitian curve in characteristic $p>0$ is determined. It is remarkable that the order of Sylow $p$-groups of the automorphism group is close to Nakajima's bound in terms of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9c5f172e0d80671f2866da910240aa62
Autor:
Herivelto Borges, Satoru Fukasawa
Publikováno v:
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP
Universidade de São Paulo (USP)
instacron:USP
We determine the distribution of Galois points for plane curves over a finite field of $q$ elements, which are Frobenius nonclassical for different powers of $q$. This family is an important class of plane curves with many remarkable properties. It c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::30d180b35a0356aea809577d0715df0d
Publikováno v:
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP
Universidade de São Paulo (USP)
instacron:USP
In connection with Galois Theory and Algebraic Curves, this paper investigates rational functions $h(x) = f(x)/g(x) \in \mathbb{F}_q(x)$ for which the value set $V_h = {\{h(α) | α \in \mathbb{F}_q \cup\{\infty\}}\}$ is relatively small. In particul
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1d903de889fa3176a9bc284a8d9bbac8
Autor:
Herivelto Borges, Ricardo Conceição
Publikováno v:
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP
Universidade de São Paulo (USP)
instacron:USP
Motivated by the study of minimal value set polynomials, we construct F q -Frobenius nonclassical curves with a large number of F q -rational points. For some of these curves, we determine the Weierstrass semigroup at the unique point at infinity. In
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e949cedc6639a4f269f2a9814e00e027
https://doi.org/10.1016/j.jpaa.2017.06.002
https://doi.org/10.1016/j.jpaa.2017.06.002
On some generalized Fermat curves and chords of an affinely regular polygon inscribed in a hyperbola
Autor:
Herivelto Borges, Mariana Coutinho
Publikováno v:
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP
Universidade de São Paulo (USP)
instacron:USP
Let G be the projective plane curve defined over F q given by a X n Y n − X n Z n − Y n Z n + b Z 2 n = 0 , where a b ∉ { 0 , 1 } , and for each s ∈ { 2 , … , n − 1 } , let D s P 1 , P 2 be the base-point-free linear series cut out on G b
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5fe5d8d60b2f564f724d1c846c94359c
Autor:
Masaaki Homma, Herivelto Borges
Publikováno v:
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP
Universidade de São Paulo (USP)
instacron:USP
In 1990, Hefez and Voloch proved that the number of \(\mathbb {F}_q\)-rational points on a nonsingular plane q-Frobenius nonclassical curve of degree d is \(N=d(q-d+2)\). We address these curves in the singular setting. In particular, we prove that \
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b2555d4b582ae3dd9abe6d94f7a09d58
https://doi.org/10.1007/s00574-016-0008-6
https://doi.org/10.1007/s00574-016-0008-6
Autor:
Herivelto Borges
Publikováno v:
Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual)
Universidade de São Paulo (USP)
instacron:USP
Universidade de São Paulo (USP)
instacron:USP
We establish a relation between minimal value set polynomials defined over F q and certain q -Frobenius nonclassical curves. The connection leads to a characterization of the curves of type g ( y ) = f ( x ) , whose irreducible components are q -Frob
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ef25e2f6318ee3193b09a472abe47555
https://doi.org/10.1016/j.jnt.2015.07.006
https://doi.org/10.1016/j.jnt.2015.07.006