On the Minimal Number of Small Elements Generating Finite Prime Fields

Marc Munsch

doi:10.1017/S000497271700048X

On the Minimal Number of Small Elements Generating Finite Prime Fields

Marc Munsch^*

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

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

Abstract

In this note, we give an upper bound for the number of elements from the interval necessary to generate the finite field with an odd prime. The general result depends on the distribution of the divisors of and can be used to deduce results which hold for almost all primes.

Original language	English
Pages (from-to)	177-184
Number of pages	8
Journal	Bulletin of the Australian Mathematical Society
Volume	96
Issue number	2
DOIs	https://doi.org/10.1017/S000497271700048X
Publication status	Published - 2017

Keywords

algorithmic number theory
character sum
generating set
Phrases finite field
primitive root
sieve theory

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1017/S000497271700048X

Cite this

@article{ae2a9b70c26b4fd79dc6dbb294c386c6,

title = "On the Minimal Number of Small Elements Generating Finite Prime Fields",

abstract = "In this note, we give an upper bound for the number of elements from the interval necessary to generate the finite field with an odd prime. The general result depends on the distribution of the divisors of and can be used to deduce results which hold for almost all primes.",

keywords = "algorithmic number theory, character sum, generating set, Phrases finite field, primitive root, sieve theory",

author = "Marc Munsch",

year = "2017",

doi = "10.1017/S000497271700048X",

language = "English",

volume = "96",

pages = "177--184",

journal = "Bulletin of the Australian Mathematical Society",

issn = "0004-9727",

publisher = "Cambridge University Press",

number = "2",

}

TY - JOUR

T1 - On the Minimal Number of Small Elements Generating Finite Prime Fields

AU - Munsch, Marc

PY - 2017

Y1 - 2017

N2 - In this note, we give an upper bound for the number of elements from the interval necessary to generate the finite field with an odd prime. The general result depends on the distribution of the divisors of and can be used to deduce results which hold for almost all primes.

AB - In this note, we give an upper bound for the number of elements from the interval necessary to generate the finite field with an odd prime. The general result depends on the distribution of the divisors of and can be used to deduce results which hold for almost all primes.

KW - algorithmic number theory

KW - character sum

KW - generating set

KW - Phrases finite field

KW - primitive root

KW - sieve theory

UR - http://www.scopus.com/inward/record.url?scp=85032508267&partnerID=8YFLogxK

U2 - 10.1017/S000497271700048X

DO - 10.1017/S000497271700048X

M3 - Article

AN - SCOPUS:85032508267

SN - 0004-9727

VL - 96

SP - 177

EP - 184

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -

On the Minimal Number of Small Elements Generating Finite Prime Fields

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this