Analytic Number Theory: Exploring the Anatomy of Integers (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 134)

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. Content: ""Cover"" ""Title page"" ""Contents"" ""Preface"" ""Notation"" ""Frequently used functions"" ""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 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"" ""Back Cover"" Frequently Used Functions -- 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 Pimes In Arithmetic Progression -- The Index Of Composition Of An Integer -- Appendix: Basic Complex Analysis Theory -- Solutions To Even-numbered Problems. Jean-marie De Koninck, Florian Luca. Includes Bibliographical References (p. 405-411) And Index.