Anatomy of Integers (CRM Proceedings & Lecture Notes) (CRM Proceedings & Lecture Notes, 46) - Softcover
The book is mostly devoted to the study of the prime factors of integers, their size and their quantity, to good bounds on the number of integers with different properties (for example, those with only large prime factors) and to the distribution of divisors of integers in a given interval. In particular, various estimates concerning smooth numbers are developed. A large emphasis is put on the study of additive and multiplicative functions as well as various arithmetic functions such as the partition function. More specific topics include the Erdos-Kac Theorem, cyclotomic polynomials, combinatorial methods, quadratic forms, zeta functions, Dirichlet series and $L$-functions. All these create an intimate understanding of the properties of integers and lead to fascinating and unexpected consequences. The volume includes contributions from leading participants in this active area of research, such as Kevin Ford, Carl Pomerance, Kannan Soundararajan and Gerald Tenenbaum.
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Review:
[I]t is quite satisfying to read in these papers some pretty descriptions of the insights behind the methods of proof, so that the application of technical anatomical results seems natural rather than confounding. --Greg Martin, University of British Columbia
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- PublisherAmerican Mathematical Society
- Publication date2008
- ISBN 10 0821844067
- ISBN 13 9780821844069
- BindingPaperback
- Number of pages297
- EditorJean-marie De Koninck, Andrew Granville, Florian Luca
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