| Softcover ISBN: | 978-1-4704-7821-6 |
| Product Code: | GSM/163.S |
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| eBook ISBN: | 978-1-4704-2223-3 |
| Product Code: | GSM/163.E |
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| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-7821-6 |
| eBook: ISBN: | 978-1-4704-2223-3 |
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| List Price: | $174.00 $131.50 |
| MAA Member Price: | $156.60 $118.35 |
| AMS Member Price: | $139.20 $105.20 |
| Softcover ISBN: | 978-1-4704-7821-6 |
| Product Code: | GSM/163.S |
| List Price: | $89.00 |
| MAA Member Price: | $80.10 |
| AMS Member Price: | $71.20 |
| eBook ISBN: | 978-1-4704-2223-3 |
| Product Code: | GSM/163.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Softcover ISBN: | 978-1-4704-7821-6 |
| eBook ISBN: | 978-1-4704-2223-3 |
| 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 |
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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 up-to-date 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.
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Table of Contents
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Part I. Elementary methods
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Chapter I.0. Some tools from real analysis
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Chapter I.1. Prime numbers
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Chapter I.2. Arithmetic functions
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Chapter I.3. Average orders
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Chapter I.4. Sieve methods
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Chapter I.5. Extremal orders
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Chapter I.6. The method of van der Corput
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Chapter I.7. Diophantine approximation
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Part II. Complex analysis methods
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Chapter II.0. The Euler gamma function
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Chapter II.1. Generating functions: Dirichlet series
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Chapter II.2. Summation formulae
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Chapter II.3. The Riemann zeta function
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Chapter II.4. The prime number theorem and the Riemann hypothesis
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Chapter II.5. The Selberg-Delange method
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Chapter II.6. Two arithmetic applications
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Chapter II.7. Tauberian theorems
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Chapter II.8. Primes in arithmetic progressions
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Part III. Probabilistic methods
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Chapter III.1. Densities
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Chapter III.2. Limiting distributions of arithmetic functions
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Chapter III.3. Normal order
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Chapter III.4. Distribution of additive functions and mean values of multiplicative functions
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Chapter III.5. Friable integers. The saddle-point method
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Chapter III.6. Integers free of small factors
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Additional Material
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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 up-to-date 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 Selberg-Delange 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 saddle-point method
-
Chapter III.6. Integers free of small factors
