| Softcover ISBN: | 978-1-4704-7203-0 |
| Product Code: | STML/104 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-1-4704-7424-9 |
| Product Code: | STML/104.E |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| Softcover ISBN: | 978-1-4704-7203-0 |
| eBook: ISBN: | 978-1-4704-7424-9 |
| Product Code: | STML/104.B |
| List Price: | $118.00 $88.50 |
| Softcover ISBN: | 978-1-4704-7203-0 |
| Product Code: | STML/104 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-1-4704-7424-9 |
| Product Code: | STML/104.E |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| Softcover ISBN: | 978-1-4704-7203-0 |
| eBook ISBN: | 978-1-4704-7424-9 |
| Product Code: | STML/104.B |
| List Price: | $118.00 $88.50 |
-
Book DetailsStudent Mathematical LibraryVolume: 104; 2023; 257 ppMSC: Primary 11
The circle method, pioneered by Ramanujan and Hardy in the early 20th century, has over the past 100 years become part of the standard tool chest of analytic number theory. Its scope of applications is ever-expanding, and the subject continues to see important breakthroughs.
This book provides an introduction to the circle method that is accessible to undergraduate students with no background in number theory. The authors' goal is to show the students the elegance of the circle method and at the same time give a complete solution of the famous Waring problem as an illustration of the method.
The first half of this book is a curated introduction to elementary number theory with an emphasis on topics needed for the second half. The second half showcases the two most “classic” applications of the circle method, to Waring's problem (following Hardy–Littlewood–Hua) and to Goldbach's conjectures (following Vinogradov, with improvements by Vaughan).
This text is suitable for a one-semester undergraduate course or for independent study and will be a great entry point into this fascinating area of research.
ReadershipUndergraduate and graduate students and researchers interested in the circle method, the Hardy-Littlewood method, Waring's problem, and Goldbach conjectures.
-
Table of Contents
-
Chapters
-
Introduction and overview
-
Fundamental theorem for arithmetic
-
Arithmetic functions
-
Introduction to congruence arithmetic
-
Distribution of prime numbers
-
An introduction to Waring’s problem
-
Waring’s problem
-
Exponential sums
-
The circle method and Waring’s problem
-
The circle method and the Goldbach conjectures
-
Epilogue
-
-
Additional Material
-
Reviews
-
The present book is aimed at upper-division undergraduates and beginning graduate students, and explains everything from scratch and writes out nearly all of the calculations. Despite the power of the method, it is not conceptually difficult, nor does its application require any advanced knowledge (beyond elementary number theory and a little complex analysis), but the proofs are very intricate and understanding them requires close attention. I think the book does a good job of explaining the method and the two applications.
Allen Stenger, MAA Reviews
-
-
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 courseAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
The circle method, pioneered by Ramanujan and Hardy in the early 20th century, has over the past 100 years become part of the standard tool chest of analytic number theory. Its scope of applications is ever-expanding, and the subject continues to see important breakthroughs.
This book provides an introduction to the circle method that is accessible to undergraduate students with no background in number theory. The authors' goal is to show the students the elegance of the circle method and at the same time give a complete solution of the famous Waring problem as an illustration of the method.
The first half of this book is a curated introduction to elementary number theory with an emphasis on topics needed for the second half. The second half showcases the two most “classic” applications of the circle method, to Waring's problem (following Hardy–Littlewood–Hua) and to Goldbach's conjectures (following Vinogradov, with improvements by Vaughan).
This text is suitable for a one-semester undergraduate course or for independent study and will be a great entry point into this fascinating area of research.
Undergraduate and graduate students and researchers interested in the circle method, the Hardy-Littlewood method, Waring's problem, and Goldbach conjectures.
-
Chapters
-
Introduction and overview
-
Fundamental theorem for arithmetic
-
Arithmetic functions
-
Introduction to congruence arithmetic
-
Distribution of prime numbers
-
An introduction to Waring’s problem
-
Waring’s problem
-
Exponential sums
-
The circle method and Waring’s problem
-
The circle method and the Goldbach conjectures
-
Epilogue
-
The present book is aimed at upper-division undergraduates and beginning graduate students, and explains everything from scratch and writes out nearly all of the calculations. Despite the power of the method, it is not conceptually difficult, nor does its application require any advanced knowledge (beyond elementary number theory and a little complex analysis), but the proofs are very intricate and understanding them requires close attention. I think the book does a good job of explaining the method and the two applications.
Allen Stenger, MAA Reviews
