Character sums with exponential functions and their applications / Sergei V. Konyagin, Igor E. Shparlinski.

Format:

Book

Author/Creator:

Koni︠a︡gin, S. V. (Sergeĭ Vladimirovich), author.

Shparlinski, Igor E., author.

Series:

Cambridge tracts in mathematics ; 136.

Cambridge tracts in mathematics ; 136

Language:

English

Subjects (All):

Exponential sums.

Physical Description:

1 online resource (viii, 163 pages) : digital, PDF file(s).

Edition:

1st ed.

Other Title:

Character Sums with Exponential Functions & their Applications

Place of Publication:

Cambridge : Cambridge University Press, 1999.

Language Note:

English

Summary:

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.

Contents:

pt. 1. Preliminaries

1. Introduction

2. Notation and Auxiliary Results

pt. 2. 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

pt. 3. Multiplicative Translations of Sets

7. Multiplicative Translations of Subgroups of F*[subscript p]

8. Multiplicative Translations of Arbitrary Sets Modulo p

pt. 4. Applications to Algebraic Number Fields

9. Representatives of Residue Classes

10. Cyclotomic Fields and Gaussian Periods

pt. 5. Applications to Pseudo-Random Number Generators

11. Prediction of Pseudo-Random Number Generators

12. Congruential Pseudo-Random Number Generators

pt. 6. Applications to Finite Fields

13. Small mth Roots Modulo p

14. Supersingular Hyperelliptic Curves

15. Distribution of Powers of Primitive Roots

pt. 7. Applications to Coding Theory and Combinatorics

16. Difference Sets in V[subscript p]

17. Dimension of BCH Codes

18. An Enumeration Problem in Finite Fields.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 157-161) and index.

ISBN:

1-107-12817-X

1-280-43245-4

9786610432455

0-511-17763-1

0-511-04036-9

0-511-14804-6

0-511-33017-0

0-511-54293-3

0-511-05179-4

OCLC:

559323775