Subgroups generated by rational functions in finite fields

Domingo Gómez-Pérez; Igor E. Shparlinski

doi:10.1007/s00605-014-0697-0

Subgroups generated by rational functions in finite fields

Domingo Gómez-Pérez^*, Igor E. Shparlinski

^*Corresponding author for this work

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

9 Citations (Scopus)

Abstract

For a large prime p, a rational function (Formula presented.) over the finite field (Formula presented.) of p elements, and integers u and H≥1, we obtain a lower bound on the number consecutive values (Formula presented.) that belong to a given multiplicative subgroup of (Formula presented.).

Original language	English
Pages (from-to)	241-253
Number of pages	13
Journal	Monatshefte fur Mathematik
Volume	176
Issue number	2
DOIs	https://doi.org/10.1007/s00605-014-0697-0
Publication status	Published - Feb 2015
Externally published	Yes

Keywords

Finite fields
Multiplicative subgroups
Polynomial congruences
Value sets of polynomials

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10.1007/s00605-014-0697-0

Cite this

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title = "Subgroups generated by rational functions in finite fields",

abstract = "For a large prime p, a rational function (Formula presented.) over the finite field (Formula presented.) of p elements, and integers u and H≥1, we obtain a lower bound on the number consecutive values (Formula presented.) that belong to a given multiplicative subgroup of (Formula presented.).",

keywords = "Finite fields, Multiplicative subgroups, Polynomial congruences, Value sets of polynomials",

author = "Domingo G{\'o}mez-P{\'e}rez and Shparlinski, {Igor E.}",

year = "2015",

month = feb,

doi = "10.1007/s00605-014-0697-0",

language = "English",

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journal = "Monatshefte fur Mathematik",

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T1 - Subgroups generated by rational functions in finite fields

AU - Gómez-Pérez, Domingo

AU - Shparlinski, Igor E.

PY - 2015/2

Y1 - 2015/2

N2 - For a large prime p, a rational function (Formula presented.) over the finite field (Formula presented.) of p elements, and integers u and H≥1, we obtain a lower bound on the number consecutive values (Formula presented.) that belong to a given multiplicative subgroup of (Formula presented.).

AB - For a large prime p, a rational function (Formula presented.) over the finite field (Formula presented.) of p elements, and integers u and H≥1, we obtain a lower bound on the number consecutive values (Formula presented.) that belong to a given multiplicative subgroup of (Formula presented.).

KW - Finite fields

KW - Multiplicative subgroups

KW - Polynomial congruences

KW - Value sets of polynomials

UR - http://www.scopus.com/inward/record.url?scp=84922003014&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP130100237

UR - http://purl.org/au-research/grants/arc/DP140100118

U2 - 10.1007/s00605-014-0697-0

DO - 10.1007/s00605-014-0697-0

M3 - Article

AN - SCOPUS:84922003014

SN - 0026-9255

VL - 176

SP - 241

EP - 253

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 2

ER -

Subgroups generated by rational functions in finite fields

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New Applications of Additive Combinatorics in Number Theory and Graph Theory

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Subgroups generated by rational functions in finite fields

Abstract

Keywords

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New Applications of Additive Combinatorics in Number Theory and Graph Theory

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