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Full Description
The authors assemble a fascinating collection of topics from analytic number theory that provides an introduction to the subject with a very clear and unique focus on the anatomy of integers, that is, on the study of the multiplicative structure of the integers. Some of the most important topics presented are the global and local behavior of arithmetic functions, an extensive study of smooth numbers, the Hardy-Ramanujan and Landau theorems, characters and the Dirichlet theorem, the $abc$ conjecture along with some of its applications, and sieve methods. The book concludes with a whole chapter on the index of composition of an integer.
One of this book's best features is the collection of problems at the end of each chapter that have been chosen carefully to reinforce the material. The authors include solutions to the even-numbered problems, making this volume very appropriate for readers who want to test their understanding of the theory presented in the book.
Contents
Preliminary notions
Prime numbers and their properties
The Riemann zeta function
Setting the stage for the proof of the prime number theorem
The proof of the prime number theorem
The global behavior of arithmetic functions
The local behavior of arithmetic functions
The fascinating Euler function
Smooth numbers
The Hardy-Ramanujan and Landau theorems
The $abc$ conjecture and some of its applications
Sieve methods
Prime numbers in arithmetic progression
Characters and the Dirichlet theorem
Selected applications of primes in arithmetic progression
The index of composition of an integer
Appendix. Basic complex analysis theory
Solutions to even-numbered problems
Bibliography
Index
