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Softcover ISBN:  9781470478216 
Product Code:  GSM/163.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470422233 
Product Code:  GSM/163.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470478216 
eBook ISBN:  9781470422233 
Product Code:  GSM/163.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 

Book DetailsGraduate Studies in MathematicsVolume: 163; 2015; 629 ppMSC: Primary 11
This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics.
Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems.
This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on uptodate bibliography.
The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate.
—Mathematical Reviews
ReadershipGraduate students and research mathematicians interested in number theory, analysis, and probability.

Table of Contents

Part I. Elementary methods

Chapter I.0. Some tools from real analysis

Chapter I.1. Prime numbers

Chapter I.2. Arithmetic functions

Chapter I.3. Average orders

Chapter I.4. Sieve methods

Chapter I.5. Extremal orders

Chapter I.6. The method of van der Corput

Chapter I.7. Diophantine approximation

Part II. Complex analysis methods

Chapter II.0. The Euler gamma function

Chapter II.1. Generating functions: Dirichlet series

Chapter II.2. Summation formulae

Chapter II.3. The Riemann zeta function

Chapter II.4. The prime number theorem and the Riemann hypothesis

Chapter II.5. The SelbergDelange method

Chapter II.6. Two arithmetic applications

Chapter II.7. Tauberian theorems

Chapter II.8. Primes in arithmetic progressions

Part III. Probabilistic methods

Chapter III.1. Densities

Chapter III.2. Limiting distributions of arithmetic functions

Chapter III.3. Normal order

Chapter III.4. Distribution of additive functions and mean values of multiplicative functions

Chapter III.5. Friable integers. The saddlepoint method

Chapter III.6. Integers free of small factors


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This book provides a self contained, thorough introduction to the analytic and probabilistic methods of number theory. The prerequisites being reduced to classical contents of undergraduate courses, it offers to students and young researchers a systematic and consistent account on the subject. It is also a convenient tool for professional mathematicians, who may use it for basic references concerning many fundamental topics.
Deliberately placing the methods before the results, the book will be of use beyond the particular material addressed directly. Each chapter is complemented with bibliographic notes, useful for descriptions of alternative viewpoints, and detailed exercises, often leading to research problems.
This third edition of a text that has become classical offers a renewed and considerably enhanced content, being expanded by more than 50 percent. Important new developments are included, along with original points of view on many essential branches of arithmetic and an accurate perspective on uptodate bibliography.
The author has made important contributions to number theory and his mastery of the material is reflected in the exposition, which is lucid, elegant, and accurate.
—Mathematical Reviews
Graduate students and research mathematicians interested in number theory, analysis, and probability.

Part I. Elementary methods

Chapter I.0. Some tools from real analysis

Chapter I.1. Prime numbers

Chapter I.2. Arithmetic functions

Chapter I.3. Average orders

Chapter I.4. Sieve methods

Chapter I.5. Extremal orders

Chapter I.6. The method of van der Corput

Chapter I.7. Diophantine approximation

Part II. Complex analysis methods

Chapter II.0. The Euler gamma function

Chapter II.1. Generating functions: Dirichlet series

Chapter II.2. Summation formulae

Chapter II.3. The Riemann zeta function

Chapter II.4. The prime number theorem and the Riemann hypothesis

Chapter II.5. The SelbergDelange method

Chapter II.6. Two arithmetic applications

Chapter II.7. Tauberian theorems

Chapter II.8. Primes in arithmetic progressions

Part III. Probabilistic methods

Chapter III.1. Densities

Chapter III.2. Limiting distributions of arithmetic functions

Chapter III.3. Normal order

Chapter III.4. Distribution of additive functions and mean values of multiplicative functions

Chapter III.5. Friable integers. The saddlepoint method

Chapter III.6. Integers free of small factors