Character sums with exponential functions and their applications
著者
書誌事項
Character sums with exponential functions and their applications
（Cambridge tracts in mathematics, 132 [i.e. 136]）
Cambridge University Press, 1999
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注記
"Cambridge tracts in mathematics 136"--Jacket
Bibliography: p. 157-161
Includes index
内容説明・目次
内容説明
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.
目次
- 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.
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