Lacunary Polynomials Over Finite Fields
eBook - PDF

Lacunary Polynomials Over Finite Fields

  1. 268 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

Lacunary Polynomials Over Finite Fields

Book details
Table of contents
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About This Book

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.

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Information

Publisher
North Holland
Year
2014
ISBN
9781483257839
Topic
Mathematics
Subtopic
Algebra
Index
Mathematics

Table of contents

  1. Front Cover
  2. Lacunary Polynomials Over Finite Fields
  3. Copyright Page
  4. Table of Contents
  5. Preface
  6. Chapter I. Preliminaries and formulation of Problems I, II, III
  7. Chapter II. Problem I
  8. Chapter III. Reduction of Problem II to Problem III
  9. Chapter IV. Problem III
  10. Chapter V. The solution of Problem II in almost all cases
  11. Chapter 6. Applications
  12. Some unsolved problems
  13. Literature
  14. Subject index
  15. List of theorems, lemmas and propositions