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Character Sums with Exponential Functions and their Applications

Character Sums with Exponential Functions and their Applications

£57.00

Part of Cambridge Tracts in Mathematics

  • Date Published: September 1999
  • availability: Available
  • format: Hardback
  • isbn: 9780521642637

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About the Authors
  • The theme of this book is the study of the distribution of integer powers modulo a prime number. It provides numerous new, sometimes quite unexpected, links between number theory and computer science as well as to other areas of mathematics. Possible applications include (but are not limited to) complexity theory, random number generation, cryptography, and coding theory. The main method discussed is based on bounds of exponential sums. Accordingly, the book contains many estimates of such sums, including new estimates of classical Gaussian sums. It also contains many open questions and proposals for further research.

    • The book contains a variety of very recent results
    • There are applications to several areas of mathematics and computer science
    • Most of the book is accessible to graduate students
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    Product details

    • Date Published: September 1999
    • format: Hardback
    • isbn: 9780521642637
    • length: 172 pages
    • dimensions: 229 x 152 x 11 mm
    • weight: 0.4kg
    • availability: Available
  • Table of Contents

    Part I. Preliminaries:
    1. Introduction
    2. Notation and auxiliary results
    Part II. Bounds of Character Sums:
    3. Bounds of long character sums
    4. Bounds of short character sums
    5. Bounds of character sums for almost all moduli
    6. Bounds of Gaussian sums
    Part III. Multiplicative Translations of Sets:
    7. Multiplicative translations of subgroups of F*p
    8. Multiplicative translations of arbitrary sets modulo p
    Part IV. Applications to Algebraic Number Fields:
    9 Representatives of residue classes
    10. Cyclotomic fields and Gaussian periods
    Part V. Applications to Pseudo-random Number Generators:
    11. Prediction of pseudo-random number generators
    12. Congruential pseudo-random number generators
    Part VI. Applications to Finite Fields:
    13. Small mth roots modulo p
    14. Supersingular hyperelliptic curves
    15. Distribution of powers of primitive roots
    16. Difference sets in Vp
    17. Dimension of BCH codes
    18. An enumeration problem in finite fields.

  • Authors

    Sergei Konyagin, Moscow State University

    Igor Shparlinski, Macquarie University, Sydney

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