Introduction to the circle method
Murty, M. Ram
Introduction to the circle method - Providence, Rhode Island: American Mathematical Society, 2023. - xix, 257p.: pbk.: 22cm - Student Mathematical Library, Volume 104 .
Includes bibliography & index.
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.
https://bookstore.ams.org/view?ProductCode=STML/104#:~:text=The%20circle%20method%2C%20pioneered%20by,continues%20to%20see%20important%20breakthroughs.
9781470472030
Number Theory
Linear Algebraic Groups
Arithmetic Functions
Goldbach Conjectures
Mathematics
Prime Numbers
512.7 MUR
Introduction to the circle method - Providence, Rhode Island: American Mathematical Society, 2023. - xix, 257p.: pbk.: 22cm - Student Mathematical Library, Volume 104 .
Includes bibliography & index.
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.
https://bookstore.ams.org/view?ProductCode=STML/104#:~:text=The%20circle%20method%2C%20pioneered%20by,continues%20to%20see%20important%20breakthroughs.
9781470472030
Number Theory
Linear Algebraic Groups
Arithmetic Functions
Goldbach Conjectures
Mathematics
Prime Numbers
512.7 MUR
