On irreducible polynomials of small height over finite fields

I. E. Shparlinski

doi:10.1007/BF01293260

On irreducible polynomials of small height over finite fields

I. E. Shparlinski^*

^*Corresponding author for this work

School of Computing

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

1 Citation (Scopus)

Abstract

It is shown that, for an arbitrary function θ(x)→ ∞, for almost all prime numbers p of any interval of the form [N - N7/ ^{12 + ε}, N] there exists an irreducible modulo p polynomial with coefficients of order O(θ(p)).

Original language	English
Pages (from-to)	427-431
Number of pages	5
Journal	Applicable Algebra in Engineering, Communications and Computing
Volume	7
Issue number	6
DOIs	https://doi.org/10.1007/BF01293260
Publication status	Published - Oct 1996

Keywords

Distribution of prime numbers
Finite fields
Irreducible polynomials

Access to Document

10.1007/BF01293260

Cite this

@article{03d3af17444a4eb19dfc90a8d00bc4be,

title = "On irreducible polynomials of small height over finite fields",

abstract = "It is shown that, for an arbitrary function θ(x)→ ∞, for almost all prime numbers p of any interval of the form [N - N7/ 12 + ε, N] there exists an irreducible modulo p polynomial with coefficients of order O(θ(p)).",

keywords = "Distribution of prime numbers, Finite fields, Irreducible polynomials",

author = "Shparlinski, {I. E.}",

year = "1996",

month = oct,

doi = "10.1007/BF01293260",

language = "English",

volume = "7",

pages = "427--431",

journal = "Applicable Algebra in Engineering, Communications and Computing",

issn = "0938-1279",

publisher = "Springer, Springer Nature",

number = "6",

}

TY - JOUR

T1 - On irreducible polynomials of small height over finite fields

AU - Shparlinski, I. E.

PY - 1996/10

Y1 - 1996/10

N2 - It is shown that, for an arbitrary function θ(x)→ ∞, for almost all prime numbers p of any interval of the form [N - N7/ 12 + ε, N] there exists an irreducible modulo p polynomial with coefficients of order O(θ(p)).

AB - It is shown that, for an arbitrary function θ(x)→ ∞, for almost all prime numbers p of any interval of the form [N - N7/ 12 + ε, N] there exists an irreducible modulo p polynomial with coefficients of order O(θ(p)).

KW - Distribution of prime numbers

KW - Finite fields

KW - Irreducible polynomials

UR - http://www.scopus.com/inward/record.url?scp=0030357689&partnerID=8YFLogxK

U2 - 10.1007/BF01293260

DO - 10.1007/BF01293260

M3 - Article

SN - 0938-1279

VL - 7

SP - 427

EP - 431

JO - Applicable Algebra in Engineering, Communications and Computing

JF - Applicable Algebra in Engineering, Communications and Computing

IS - 6

ER -

On irreducible polynomials of small height over finite fields

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this