Character Sums with Exponential Functions and their Applications
Character Sums with Exponential Functions and their Applications
November 1999
Hardback
9780521642637
AUD$214.95
inc GSTHardback
USD
eBook
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
Product details
January 2007Adobe eBook Reader
9780511036569
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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.
