2016
DOI: 10.1007/s00574-016-0008-6
|View full text |Cite
|
Sign up to set email alerts
|

Points on singular Frobenius nonclassical curves

Abstract: In 1990, Hefez and Voloch proved that the number of Fq-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 d(q − d + 2) is a lower bound on the number of Fq-rational points on such curves of degree d.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1
1

Citation Types

0
10
0

Year Published

2018
2018
2024
2024

Publication Types

Select...
7
1

Relationship

2
6

Authors

Journals

citations
Cited by 12 publications
(10 citation statements)
references
References 7 publications
0
10
0
Order By: Relevance
“…Either C has a singular point or not. Since N < q 3 + 1, the curve C is Frobenius classical from [6,Corollary 1.4]. Therefore, we can apply the Stöhr and Voloch's estimate for the number of rational points of a Frobenius classical curve [17, Theorem 1.1] obtaining…”
Section: Lemma 25 ([7]mentioning
confidence: 99%
“…Either C has a singular point or not. Since N < q 3 + 1, the curve C is Frobenius classical from [6,Corollary 1.4]. Therefore, we can apply the Stöhr and Voloch's estimate for the number of rational points of a Frobenius classical curve [17, Theorem 1.1] obtaining…”
Section: Lemma 25 ([7]mentioning
confidence: 99%
“…8.1. Genus and p-rank of the irreducible plane curve of homogeneous equation (6). In this section, λ ∈ {0, 1, −1}, and Y = C λ stands for the nonsingular plane curve with homogeneous equation (6), and Aut(Y) for the automorphism group of Y.…”
Section: Nonclassicality Of G-invariant Irreducible Plane Curvesmentioning
confidence: 99%
“…Frobenius non-classical curves are somewhat rare; see [3,21]. In some cases, they have many points over F q ; see [1,4,10,21]. Also, they are closely related to univariate polynomials with minimal values sets, see [2].…”
Section: Background On Non-classical Plane Curvesmentioning
confidence: 99%