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Analytic Number Theory: Exploring the Anatomy of Integers
Jean-Marie De Koninck, Université Laval, Quebec, QC, Canada, and Florian Luca, Universidad Nacional Autonoma de México, Morelia, Michoacan, México

Graduate Studies in Mathematics
2012; 414 pp; hardcover
Volume: 134
ISBN-10: 0-8218-7577-9
ISBN-13: 978-0-8218-7577-3
List Price: US$75
Member Price: US$60
Order Code: GSM/134
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See also:

Anatomy of Integers - Jean-Marie De Koninck, Andrew Granville and Florian Luca

Analytic Number Theory - Henryk Iwaniec and Emmanuel Kowalski

Not Always Buried Deep: A Second Course in Elementary Number Theory - Paul Pollack

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.

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Graduate students and research mathematicians interested in analytic number theory.

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