Introduction to the circle method
Material type:
TextLanguage: English Series: Student mathematical library ; volume 104Publication details: Rhode Island : American Mathematical Society, 2023. Description: xix, 257pISBN: 9781470472030Subject(s): Hardy-Littlewood method | Waring's problem | Number theory -- Additive number theory; partitions -- Applications of the Hardy-Littlewood method | Number theory -- Additive number theory; partitions -- Goldbach-type theorems; other additive questions involving primes | Number theory -- Forms and linear algebraic groups -- Sums of squares and representations by other particular quadratic formsDDC classification: 511 Online resources: Table of Contents | Reviews 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.
| Item type | Current library | Call number | Status | Date due | Barcode |
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Book
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SMS Library | 511 MUR-I (Browse shelf(Opens below)) | Available | 25203 |
Includes bibliographical references and 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.
Undergraduate and graduate students and researchers interested in the circle method, the Hardy-Littlewood method, Waring's problem, and Goldbach conjectures.
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