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  3. Character Sums with Exponential Functions and their Applications
  • Cited by 96
Publisher:
Cambridge University Press
Online publication date:
August 2010
Print publication year:
1999
Online ISBN:
9780511542930
DOI:
https://doi.org/10.1017/CBO9780511542930
Subjects:
Mathematics (general), Mathematics, Number Theory
Series:
Cambridge Tracts in Mathematics (136)
Information

Book description

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.

Reviews

"It is perhaps surprising that such a diverse collections of problems may be unified under one theme. This book should serve as a useful reference for mathematicians interested in such problems as well as a valuable source of open questions for research projects." Bulletin of the American Mathematical Society

"...this is a work that should be present in any decent mathematical library." Mathematical Reviews

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