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Mathematics and Its Applications

Finite Fields: Theory and Computation

The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography

Authors: Shparlinski, Igor

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eBook 91,62 €
price for Spain (gross)
  • ISBN 978-94-015-9239-0
  • Digitally watermarked, DRM-free
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  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-0-7923-5662-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 114,39 €
price for Spain (gross)
  • ISBN 978-90-481-5203-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types and new applications of finite fields to other areas of mathematics. For completeness we in­ clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener­ ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod­ ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.

Reviews

`...the book can yet be highly recommended as encyclopaedia on these topics, in particular because many Russian papers are incorporated which are hardly accessible.'
Monatschafte für Mathematik, 132:1 (2001)

Table of contents (12 chapters)

  • Introduction

    Shparlinski, Igor E.

    Pages 1-11

    Preview Buy Chapter 30,19 €
  • Links Flowchart

    Shparlinski, Igor E.

    Pages 13-15

    Preview Buy Chapter 30,19 €
  • Polynomial Factorization

    Shparlinski, Igor E.

    Pages 17-44

    Preview Buy Chapter 30,19 €
  • Finding Irreducible and Primitive Polynomials

    Shparlinski, Igor E.

    Pages 45-64

    Preview Buy Chapter 30,19 €
  • The Distribution of Irreducible, Primitive and Other Special Polynomials and Matrices

    Shparlinski, Igor E.

    Pages 65-98

    Preview Buy Chapter 30,19 €

Buy this book

eBook 91,62 €
price for Spain (gross)
  • ISBN 978-94-015-9239-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 114,39 €
price for Spain (gross)
  • ISBN 978-0-7923-5662-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 114,39 €
price for Spain (gross)
  • ISBN 978-90-481-5203-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Finite Fields: Theory and Computation
Book Subtitle
The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography
Authors
Series Title
Mathematics and Its Applications
Series Volume
477
Copyright
1999
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-015-9239-0
DOI
10.1007/978-94-015-9239-0
Hardcover ISBN
978-0-7923-5662-2
Softcover ISBN
978-90-481-5203-2
Edition Number
1
Number of Pages
XIV, 528
Topics