Introduction to the circle method

By:

Murty, M. Ram

Contributor(s):

Sinha, Kaneenika [Co-author]

Series: Student Mathematical Library, Volume 104Publication details: Providence, Rhode Island: American Mathematical Society, 2023.Description: xix, 257p.: pbk.: 22cmISBN:

9781470472030

Subject(s):

DDC classification:

512.7 MUR

Summary: 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.

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	General	512.7 MUR (Browse shelf(Opens below))	1	Checked out	15/07/2024	034076

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.

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