On the number of solutions of equations of Dickson polynomials over finite fields

Wun Seng Chou, Gary Lee Mullen, Bertram Wassermann

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Let k, n1, ..., nk be fixed positive integers, c1, ..., ck ∈ GF(q)*, and a1, ..., ak, c ∈ GF(q). We study the number of solutions in GF(q) of the equation c1Dn1(x1, a1)+c2Dn2(x2, a2)+...+ckDnk(xk, ak) = c, where each Dni(xi, ai), 1 ≤ i ≤ k, is the Dickson polynomial of degree ni with parameter ai. We also employ the results of the k = 1 case to recover the cardinality of preimages and images of Dickson polynomials obtained earlier by Chou, Gomez-Calderon and Mullen [1].

Original languageEnglish (US)
Pages (from-to)917-931
Number of pages15
JournalTaiwanese Journal of Mathematics
Volume12
Issue number4
DOIs
StatePublished - Jan 1 2008

Fingerprint

Dickson Polynomials
Number of Solutions
Galois field
Cardinality
Integer

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{ccb38f02214d4356b3e4c1f730805523,
title = "On the number of solutions of equations of Dickson polynomials over finite fields",
abstract = "Let k, n1, ..., nk be fixed positive integers, c1, ..., ck ∈ GF(q)*, and a1, ..., ak, c ∈ GF(q). We study the number of solutions in GF(q) of the equation c1Dn1(x1, a1)+c2Dn2(x2, a2)+...+ckDnk(xk, ak) = c, where each Dni(xi, ai), 1 ≤ i ≤ k, is the Dickson polynomial of degree ni with parameter ai. We also employ the results of the k = 1 case to recover the cardinality of preimages and images of Dickson polynomials obtained earlier by Chou, Gomez-Calderon and Mullen [1].",
author = "Chou, {Wun Seng} and Mullen, {Gary Lee} and Bertram Wassermann",
year = "2008",
month = "1",
day = "1",
doi = "10.11650/twjm/1500404986",
language = "English (US)",
volume = "12",
pages = "917--931",
journal = "Taiwanese Journal of Mathematics",
issn = "1027-5487",
publisher = "Mathematical Society of the Rep. of China",
number = "4",

}

On the number of solutions of equations of Dickson polynomials over finite fields. / Chou, Wun Seng; Mullen, Gary Lee; Wassermann, Bertram.

In: Taiwanese Journal of Mathematics, Vol. 12, No. 4, 01.01.2008, p. 917-931.

Research output: Contribution to journalArticle

TY - JOUR

T1 - On the number of solutions of equations of Dickson polynomials over finite fields

AU - Chou, Wun Seng

AU - Mullen, Gary Lee

AU - Wassermann, Bertram

PY - 2008/1/1

Y1 - 2008/1/1

N2 - Let k, n1, ..., nk be fixed positive integers, c1, ..., ck ∈ GF(q)*, and a1, ..., ak, c ∈ GF(q). We study the number of solutions in GF(q) of the equation c1Dn1(x1, a1)+c2Dn2(x2, a2)+...+ckDnk(xk, ak) = c, where each Dni(xi, ai), 1 ≤ i ≤ k, is the Dickson polynomial of degree ni with parameter ai. We also employ the results of the k = 1 case to recover the cardinality of preimages and images of Dickson polynomials obtained earlier by Chou, Gomez-Calderon and Mullen [1].

AB - Let k, n1, ..., nk be fixed positive integers, c1, ..., ck ∈ GF(q)*, and a1, ..., ak, c ∈ GF(q). We study the number of solutions in GF(q) of the equation c1Dn1(x1, a1)+c2Dn2(x2, a2)+...+ckDnk(xk, ak) = c, where each Dni(xi, ai), 1 ≤ i ≤ k, is the Dickson polynomial of degree ni with parameter ai. We also employ the results of the k = 1 case to recover the cardinality of preimages and images of Dickson polynomials obtained earlier by Chou, Gomez-Calderon and Mullen [1].

UR - http://www.scopus.com/inward/record.url?scp=77952150487&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77952150487&partnerID=8YFLogxK

U2 - 10.11650/twjm/1500404986

DO - 10.11650/twjm/1500404986

M3 - Article

AN - SCOPUS:77952150487

VL - 12

SP - 917

EP - 931

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

SN - 1027-5487

IS - 4

ER -