Cover for Lacunary Polynomials Over Finite Fields

Lacunary Polynomials Over Finite Fields

Book1973

Author:

L. RÉDEI

Lacunary Polynomials Over Finite Fields

Book1973

 

Cover for Lacunary Polynomials Over Finite Fields

Author:

L. RÉDEI

About the book

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Book description

Lacunary Polynomials Over Finite Fields focuses on reducible lacunary polynomials over finite fields, as well as stem polynomials, differential equations, and gaussian sums. The ... read full description

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  2. Book chapterAbstract only

    CHAPTER I - PRELIMINARIES AND FORMULATION OF PROBLEMS I, II, III

    Pages 1-28

  3. Book chapterAbstract only

    CHAPTER II - PROBLEM I

    Pages 29-33

  4. Book chapterAbstract only

    CHAPTER III - REDUCTION OF PROBLEM II TO PROBLEM III

    Pages 34-88

  5. Book chapterAbstract only

    CHAPTER IV - PROBLEM III

    Pages 89-178

  6. Book chapterAbstract only

    CHAPTER V - THE SOLUTION OF PROBLEM II IN ALMOST ALL CASES

    Pages 179-193

  7. Book chapterAbstract only

    CHAPTER VI - APPLICATIONS

    Pages 194-251

  8. Book chapterNo access

    SOME UNSOLVED PROBLEMS

    Pages 252-253

  9. Book chapterNo access

    LITERATURE

    Page 254

  10. Book chapterNo access

    SUBJECT INDEX

    Pages 255-256

  11. Book chapterNo access

    LIST OF THEOREMS, LEMMAS AND PROPOSITIONS

    Page 257

About the book

Description

Lacunary Polynomials Over Finite Fields focuses on reducible lacunary polynomials over finite fields, as well as stem polynomials, differential equations, and gaussian sums. The monograph first tackles preliminaries and formulation of Problems I, II, and III, including some basic concepts and notations, invariants of polynomials, stem polynomials, fully reducible polynomials, and polynomials with a restricted range. The text then takes a look at Problem I and reduction of Problem II to Problem III. Topics include reduction of the marginal case of Problem II to that of Problem III, proposition on power series, proposition on polynomials, and preliminary remarks on polynomial and differential equations. The publication ponders on Problem III and applications. Topics include homogeneous elementary symmetric systems of equations in finite fields; divisibility maximum properties of the gaussian sums and related questions; common representative systems of a finite abelian group with respect to given subgroups; and difference quotient of functions in finite fields. The monograph also reviews certain families of linear mappings in finite fields, appendix on the degenerate solutions of Problem II, a lemma on the greatest common divisor of polynomials with common gap, and two group-theoretical propositions. The text is a dependable reference for mathematicians and researchers interested in the study of reducible lacunary polynomials over finite fields.

Lacunary Polynomials Over Finite Fields focuses on reducible lacunary polynomials over finite fields, as well as stem polynomials, differential equations, and gaussian sums. The monograph first tackles preliminaries and formulation of Problems I, II, and III, including some basic concepts and notations, invariants of polynomials, stem polynomials, fully reducible polynomials, and polynomials with a restricted range. The text then takes a look at Problem I and reduction of Problem II to Problem III. Topics include reduction of the marginal case of Problem II to that of Problem III, proposition on power series, proposition on polynomials, and preliminary remarks on polynomial and differential equations. The publication ponders on Problem III and applications. Topics include homogeneous elementary symmetric systems of equations in finite fields; divisibility maximum properties of the gaussian sums and related questions; common representative systems of a finite abelian group with respect to given subgroups; and difference quotient of functions in finite fields. The monograph also reviews certain families of linear mappings in finite fields, appendix on the degenerate solutions of Problem II, a lemma on the greatest common divisor of polynomials with common gap, and two group-theoretical propositions. The text is a dependable reference for mathematicians and researchers interested in the study of reducible lacunary polynomials over finite fields.

Details

ISBN

978-0-7204-2050-0

Language

English

Published

1973

Copyright

Copyright © 1973 Elsevier Inc. All rights reserved.

Imprint

North Holland

Authors

L. RÉDEI

Member of the Hungarian, Academy of Sciences