Florian Luca

Jean-Marie De Koninck

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.

Exploring the Anatomy of Integers

Analytic Number Theory

Jaroslav Nešetřil

Richard J. Nowakowski

Melvyn B. Nathanson

Bruce M. Landman

Aaron Robertson

This volume is dedicated to the work of three leading mathematicians in combinatoric game theory, Elwyn Berlekamp, John Conway, and Richard Guy and includes 20 contributions from colleagues reflecting on their work.

A Special Collection in Honor of Elwyn Berlekamp, John H. Conway and Richard K. Guy

Combinatorial Game Theory

Andrew Granville

J. M. de Koninck

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 functionssuch 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 andunexpected 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.

Anatomy of Integers

Florian Luca

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