Differential operators and hyperelliptic curves over finite fields

Iván Blanco-Chacón; Alberto F. Boix; Stiofáin Fordham; Emrah Sercan Yilmaz

doi:10.1016/j.ffa.2018.02.007

Differential operators and hyperelliptic curves over finite fields

Iván Blanco-Chacón, Alberto F. Boix, Stiofáin Fordham, Emrah Sercan Yilmaz

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Boix, De Stefani and Vanzo have characterised ordinary/supersingular elliptic curves over F_p in terms of the level of the defining cubic homogeneous polynomial. We extend their study to arbitrary genus, in particular we prove that every ordinary hyperelliptic curve C of genus g≥2 has level 2. We provide a good number of examples and raise a conjecture.

Original language	English
Pages (from-to)	351-370
Number of pages	20
Journal	Finite Fields and their Applications
Volume	51
DOIs	https://doi.org/10.1016/j.ffa.2018.02.007
State	Published - 1 May 2018

Keywords

Algorithm
Differential operator
Frobenius map
Prime characteristic

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

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10.1016/j.ffa.2018.02.007

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title = "Differential operators and hyperelliptic curves over finite fields",

abstract = "Boix, De Stefani and Vanzo have characterised ordinary/supersingular elliptic curves over Fp in terms of the level of the defining cubic homogeneous polynomial. We extend their study to arbitrary genus, in particular we prove that every ordinary hyperelliptic curve C of genus g≥2 has level 2. We provide a good number of examples and raise a conjecture.",

keywords = "Algorithm, Differential operator, Frobenius map, Prime characteristic",

author = "Iv{\'a}n Blanco-Chac{\'o}n and Boix, {Alberto F.} and Stiof{\'a}in Fordham and Yilmaz, {Emrah Sercan}",

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AU - Blanco-Chacón, Iván

AU - Boix, Alberto F.

AU - Fordham, Stiofáin

AU - Yilmaz, Emrah Sercan

PY - 2018/5/1

Y1 - 2018/5/1

N2 - Boix, De Stefani and Vanzo have characterised ordinary/supersingular elliptic curves over Fp in terms of the level of the defining cubic homogeneous polynomial. We extend their study to arbitrary genus, in particular we prove that every ordinary hyperelliptic curve C of genus g≥2 has level 2. We provide a good number of examples and raise a conjecture.

AB - Boix, De Stefani and Vanzo have characterised ordinary/supersingular elliptic curves over Fp in terms of the level of the defining cubic homogeneous polynomial. We extend their study to arbitrary genus, in particular we prove that every ordinary hyperelliptic curve C of genus g≥2 has level 2. We provide a good number of examples and raise a conjecture.

KW - Algorithm

KW - Differential operator

KW - Frobenius map

KW - Prime characteristic

UR - http://www.scopus.com/inward/record.url?scp=85043392638&partnerID=8YFLogxK

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DO - 10.1016/j.ffa.2018.02.007

M3 - Article

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SP - 351

EP - 370

JO - Finite Fields and their Applications

JF - Finite Fields and their Applications

ER -

Differential operators and hyperelliptic curves over finite fields

Abstract

Keywords

ASJC Scopus subject areas

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