On special finite fields

Florian Luca; Igor E. Shparlinski

On special finite fields

Florian Luca^*, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

It has been shown by J.-P. Serre that the largest possible number of F(q)-rational points on curves of small genus over the finite field F, of q elements depends on the divisibility property p vertical bar [2q(1/2)], where p is the characteristic of F(q). In this paper, we obtain upper and lower bounds on the number of prime powers q

Original language	English
Title of host publication	Arithmetic, geometry, cryptography and coding theory
Editors	G Lachaud, C Ritzenthaler, MA Tsfasman
Place of Publication	USA
Publisher	AMER MATHEMATICAL SOC
Pages	163-168
Number of pages	6
ISBN (Print)	9780821847169
Publication status	Published - 2009
Event	11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory - Marseilles, France Duration: 5 Nov 2007 → 9 Nov 2007

Publication series

Name	Contemporary Mathematics
Publisher	AMER MATHEMATICAL SOC
Volume	487
ISSN (Print)	0271-4132

Conference

Conference	11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory
Country/Territory	France
City	Marseilles
Period	5/11/07 → 9/11/07

Keywords

RATIONAL-POINTS
CURVES
NUMBER
PARTS

Cite this

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title = "On special finite fields",

abstract = "It has been shown by J.-P. Serre that the largest possible number of F(q)-rational points on curves of small genus over the finite field F, of q elements depends on the divisibility property p vertical bar [2q(1/2)], where p is the characteristic of F(q). In this paper, we obtain upper and lower bounds on the number of prime powers q",

keywords = "RATIONAL-POINTS, CURVES, NUMBER, PARTS",

author = "Florian Luca and Shparlinski, {Igor E.}",

year = "2009",

language = "English",

isbn = "9780821847169",

series = "Contemporary Mathematics",

publisher = "AMER MATHEMATICAL SOC",

pages = "163--168",

editor = "G Lachaud and C Ritzenthaler and MA Tsfasman",

booktitle = "Arithmetic, geometry, cryptography and coding theory",

note = "11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory ; Conference date: 05-11-2007 Through 09-11-2007",

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TY - CHAP

T1 - On special finite fields

AU - Luca, Florian

AU - Shparlinski, Igor E.

PY - 2009

Y1 - 2009

N2 - It has been shown by J.-P. Serre that the largest possible number of F(q)-rational points on curves of small genus over the finite field F, of q elements depends on the divisibility property p vertical bar [2q(1/2)], where p is the characteristic of F(q). In this paper, we obtain upper and lower bounds on the number of prime powers q

AB - It has been shown by J.-P. Serre that the largest possible number of F(q)-rational points on curves of small genus over the finite field F, of q elements depends on the divisibility property p vertical bar [2q(1/2)], where p is the characteristic of F(q). In this paper, we obtain upper and lower bounds on the number of prime powers q

KW - RATIONAL-POINTS

KW - CURVES

KW - NUMBER

KW - PARTS

M3 - Chapter

SN - 9780821847169

T3 - Contemporary Mathematics

SP - 163

EP - 168

BT - Arithmetic, geometry, cryptography and coding theory

A2 - Lachaud, G

A2 - Ritzenthaler, C

A2 - Tsfasman, MA

PB - AMER MATHEMATICAL SOC

CY - USA

T2 - 11th Conference on Arithmetic, Geometry, Cryptography and Coding Theory

Y2 - 5 November 2007 through 9 November 2007

ER -

On special finite fields

Abstract

Publication series

Conference

Keywords

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Cite this