## Browse content

### Table of contents

#### Actions for selected chapters

- Full text access
- Book chapterAbstract only
#### CHAPTER I - PRELIMINARIES AND FORMULATION OF PROBLEMS I, II, III

Pages 1-28 - Book chapterAbstract only
#### CHAPTER II - PROBLEM I

Pages 29-33 - Book chapterAbstract only
#### CHAPTER III - REDUCTION OF PROBLEM II TO PROBLEM III

Pages 34-88 - Book chapterAbstract only
#### CHAPTER IV - PROBLEM III

Pages 89-178 - Book chapterAbstract only
#### CHAPTER V - THE SOLUTION OF PROBLEM II IN ALMOST ALL CASES

Pages 179-193 - Book chapterAbstract only
#### CHAPTER VI - APPLICATIONS

Pages 194-251 - Book chapterNo access
#### SOME UNSOLVED PROBLEMS

Pages 252-253 - Book chapterNo access
#### LITERATURE

Page 254 - Book chapterNo access
#### SUBJECT INDEX

Pages 255-256 - 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