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A Course in Analytic Number Theory

Marius Overholt University of Tromso, Tromso, Norway
Available Formats:
Hardcover ISBN: 978-1-4704-1706-2
Product Code: GSM/160
List Price: $84.00 MAA Member Price:$75.60
AMS Member Price: $67.20 Electronic ISBN: 978-1-4704-2041-3 Product Code: GSM/160.E List Price:$79.00
MAA Member Price: $71.10 AMS Member Price:$63.20
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List Price: $126.00 MAA Member Price:$113.40
AMS Member Price: $100.80 Click above image for expanded view A Course in Analytic Number Theory Marius Overholt University of Tromso, Tromso, Norway Available Formats:  Hardcover ISBN: 978-1-4704-1706-2 Product Code: GSM/160  List Price:$84.00 MAA Member Price: $75.60 AMS Member Price:$67.20
 Electronic ISBN: 978-1-4704-2041-3 Product Code: GSM/160.E
 List Price: $79.00 MAA Member Price:$71.10 AMS Member Price: $63.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$126.00 MAA Member Price: $113.40 AMS Member Price:$100.80
• Book Details

Volume: 1602014; 371 pp
MSC: Primary 11;

This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem.

The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader.

The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.

Graduate students interested in number theory.

• Chapters
• Chapter 1. Arithmetic functions
• Chapter 2. Topics on arithmetic functions
• Chapter 3. Characters and Euler products
• Chapter 4. The circle method
• Chapter 5. The method of contour integrals
• Chapter 6. The prime number theorem
• Chapter 7. The Siegel-Walfisz theorem
• Chapter 8. Mainly analysis
• Chapter 9. Euler products and number fields
• Chapter 10. Explicit formulas
• Chapter 11. Supplementary exercises

• Reviews

• This book is a proper text for a graduate student (with a pretty strong background) keen on getting into analytic number theory, and it's quite a good one. It's well-written, rather exhaustive, and well-paced. The choice of themes is good, too, and will form a very sound platform for future studies and work in this gorgeous field.

MAA Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1602014; 371 pp
MSC: Primary 11;

This book is an introduction to analytic number theory suitable for beginning graduate students. It covers everything one expects in a first course in this field, such as growth of arithmetic functions, existence of primes in arithmetic progressions, and the Prime Number Theorem. But it also covers more challenging topics that might be used in a second course, such as the Siegel-Walfisz theorem, functional equations of L-functions, and the explicit formula of von Mangoldt. For students with an interest in Diophantine analysis, there is a chapter on the Circle Method and Waring's Problem. Those with an interest in algebraic number theory may find the chapter on the analytic theory of number fields of interest, with proofs of the Dirichlet unit theorem, the analytic class number formula, the functional equation of the Dedekind zeta function, and the Prime Ideal Theorem.

The exposition is both clear and precise, reflecting careful attention to the needs of the reader. The text includes extensive historical notes, which occur at the ends of the chapters. The exercises range from introductory problems and standard problems in analytic number theory to interesting original problems that will challenge the reader.

The author has made an effort to provide clear explanations for the techniques of analysis used. No background in analysis beyond rigorous calculus and a first course in complex function theory is assumed.

Graduate students interested in number theory.

• Chapters
• Chapter 1. Arithmetic functions
• Chapter 2. Topics on arithmetic functions
• Chapter 3. Characters and Euler products
• Chapter 4. The circle method
• Chapter 5. The method of contour integrals
• Chapter 6. The prime number theorem
• Chapter 7. The Siegel-Walfisz theorem
• Chapter 8. Mainly analysis
• Chapter 9. Euler products and number fields
• Chapter 10. Explicit formulas
• Chapter 11. Supplementary exercises
• This book is a proper text for a graduate student (with a pretty strong background) keen on getting into analytic number theory, and it's quite a good one. It's well-written, rather exhaustive, and well-paced. The choice of themes is good, too, and will form a very sound platform for future studies and work in this gorgeous field.

MAA Reviews
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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