An Introduction to the Circle Method (Paperback)

M. Ram Murty

ISBN 10: 1470472031 / ISBN 13: 9781470472030

Published by American Mathematical Society, Providence, 2023

About this Item

Paperback. 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. 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. This book provides an introduction to the circle method that is accessible to undergraduate students with no background in number theory. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9781470472030

Bibliographic Details

• Title: An Introduction to the Circle Method (Paperback)
• Publisher: American Mathematical Society, Providence
• Publication Date: 2023
• Language: English
• ISBN 10: 1470472031
• ISBN 13: 9781470472030
• Binding: Paperback
• Condition: new

About this title

Synopsis

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.

About the Author

M. Ram Murty, Queen’s University, Kingston, Ontario, Canada, and Kaneenika Sinha, Indian Institute of Science Education and Research, Pune, Maharashtra, India