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An Introduction to the Circle Method
 
M. Ram Murty Queen’s University, Kingston, Ontario, Canada
Kaneenika Sinha Indian Institute of Science Education and Research, Pune, Maharashtra, India
Softcover ISBN:  978-1-4704-7203-0
Product Code:  STML/104
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
eBook ISBN:  978-1-4704-7424-9
Product Code:  STML/104.E
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
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
Sale Price: $70.80 $53.10
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An Introduction to the Circle Method
M. Ram Murty Queen’s University, Kingston, Ontario, Canada
Kaneenika Sinha Indian Institute of Science Education and Research, Pune, Maharashtra, India
Softcover ISBN:  978-1-4704-7203-0
Product Code:  STML/104
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
eBook ISBN:  978-1-4704-7424-9
Product Code:  STML/104.E
List Price: $59.00
Individual Price: $47.20
Sale Price: $35.40
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
Sale Price: $70.80 $53.10
  • Book Details
     
     
    Student Mathematical Library
    Volume: 1042023; 257 pp
    MSC: 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.

    Readership

    Undergraduate 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
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 1042023; 257 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
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