Ebook: Character sums with exponential functions and their applications

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.