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Character Sums with Exponential Functions and their Applicationsby Sergei Konyagin; Igor Shparlinski; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak
Cambridge University Press 1999; US$ 62.00The theme of this book is 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. Applications include (but are not limited to) complexity theory, random number generation, cryptography, and coding theory. more...
Prime Numbersby David Wells
John Wiley & Sons, Inc. 2005; US$ 24.95A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you'll... more...
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Cambridge University Press 2005; US$ 47.00This book provides a motivated introduction to sieve theory. Rather than focus on technical details which obscure the beauty of the theory, the authors focus on examples and applications, developing the theory in parallel. Suitable for a senior level undergraduate course or an introductory graduate course in analytic number theory. more...
Prime Numbersby Richard Crandall
Springer-Verlag New York Inc 2005; US$ 74.95Prime numbers beckon to the beginner, the basic notion of primality being accessible to a child. This book concentrates on the computational aspects of prime numbers, such as recognizing primes and discovering the fundamental prime factors of a given number. It includes over 100 explicit algorithms cast in detailed pseudocode. more...
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Cambridge University Press 2006; US$ 91.00Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. The authors bring their extensive and distinguished research expertise to prepare the student for intelligent reading of the more advanced research literature. more...
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Trigonometric Sums in Number Theory and Analysisby Gennady I. Arkhipov; Anatoly A. Karatsuba; Vladimir N. Chubarikov
Walter de Gruyter, Inc. 2004; US$ 200.00The book presents the theory of multiple trigonometric sums constructed by the authors. Following a unified approach, the authors obtain estimates for these sums similar to the classical I. M. Vinogradov's estimates and use them to solve several problems in analytic number theory. They investigate trigonometric integrals, which are often encountered in physics, mathematical statistics, and analysis, and present purely arithmetic results concerning the solvability of equations in integers. more...
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The Large Sieve and its Applicationsby Emmanuel Kowalski
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