Skip to content
Register Sign in Wishlist
Character Sums with Exponential Functions and their Applications

Character Sums with Exponential Functions and their Applications


Part of Cambridge Tracts in Mathematics

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

£ 99.99

Add to cart Add to wishlist

Other available formats:

Looking for an inspection copy?

This title is not currently available on inspection

Product filter button
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
    Read more

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    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

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

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.

Please fill in the required fields in your feedback submission.