Character Sums with Exponential Functions and their Applications
£99.99
Part of Cambridge Tracts in Mathematics
- Authors:
- Sergei Konyagin, Moscow State University
- Igor Shparlinski, Macquarie University, Sydney
- Date Published: September 1999
- availability: Available
- format: Hardback
- isbn: 9780521642637
£
99.99
Hardback
Other available formats:
eBook
Looking for an inspection copy?
This title is not currently available on inspection
-
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.
Read more- 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
Customer reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity
×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.
Related Books
related journals
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org
Register Sign in» Proceed
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.
Continue ×Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.
×