Dickson polynomials

by Lidl, Rudolf

Type Book

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Title Statements

Full title :Dickson polynomials / R. Lidl, G.L. Mullen, G. Turnwald.

Summary

"Dickson polynomials are closely related with Chebyshev polynomials. They have a variety of algebraic and number theoretic properties and satisfy simple second-order linear differential equations and linear recurrences. For suitable parameters they form a commutative semigroup under composition. Dickson polynomials are of fundamental importance in the theory of permutation polynomials and related topics. In particular, they serve as examples of integral polynomials which induce permutations for infinitely many primes. According to 'Schur's conjecture' there are essentially no other examples. Dickson polynomials are also important in cryptology and for pseudoprimality testing." "The book provides a comprehensive up-to-date collection of results concerning Dickson polynomials and presents several applications. It also treats generalizations to polynomials in several variables and related rational function like Redei functions. Each of the seven chapters includes exercises and notes. Tables of Dickson polynomials are given in the Appendix." "For most parts of the text only the basic theory of groups, rings and fields is required. The proof of 'Schur's Conjecture' is largely self-contained but is based on more advanced results like an estimate for the number of rational points on an absolutely irreducible curve over a finite field. Two important theorems on primitive permutation groups are supplied with complete proofs."

"The book may serve as a reference text for graduate students or researchers interested in algebraic or number theoretic aspects of polynomials and for cryptologists."--Jacket.

Edition Statements

Publication Date:1993.

Publication Statements

Publisher(s):Copublished in the United States with John Wiley & Sons, Longman Scientific & Technical
Place of Publication:Harlow, Essex, England
Language:eng
Publication Date:1993.

The Physical Object

Description:207 pages ; : 25 cm.

Edition Identifiers

ISBN:0582091195, 9780582091191
oclc:ocm26723766
LC Classification:QA404.5
Dewey Decimal:515/.55

Ch. 1. Algebraic Foundations -- Ch. 2. Basic Properties of Dickson Polynomials -- Ch. 3. Finite Fields -- Ch. 4. Integers mod m -- Ch. 5. Other Rings -- Ch. 6. The Schur Conjecture and its Converse -- Ch. 7. Applications -- Appendix. Tables of Dickson Polynomials.