Character Sums with Exponential Functions and their Applications (Cambridge Tracts in Mathematics, Series Number 136) - Hardcover

Konyagin, Sergei; Shparlinski, Igor

 
9780521642637: Character Sums with Exponential Functions and their Applications (Cambridge Tracts in Mathematics, Series Number 136)
Hardcover
ISBN 10: 0521642639 ISBN 13: 9780521642637
Publisher: Cambridge University Press, 1999

Synopsis

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.

"synopsis" may belong to another edition of this title.

Book Description

The theme of this book is the study of the distribution of integer powers modulo a prime number. It provides numerous new links between number theory and computer science as well as 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 and the book contains many estimates of these, including new estimates of classical Gaussian sums. It also contains many open questions and proposals for further research.

Review

"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

"About this title" may belong to another edition of this title.

Publisher
Cambridge University Press
Publication date
1999
Language
English
ISBN 10 
0521642639
ISBN 13 
9780521642637
Binding
Hardcover
Number of pages
172