An introduction to the circle method / M. Ram Murty, Kaneenika Sinha.
| Author/creator | Murty, Maruti Ram author. |
| Other author | Sinha, Kaneenika, 1980- author. |
| Other author | American Mathematical Society, publisher. |
| Format | Electronic |
| Publication | Providence, Rhode Island : American Mathematical Society, [2023] |
| Copyright Date | ©2023 |
| Description | 1 online resource (xix, 257 pages) : illustrations. |
| Supplemental Content | Ebook Central |
| Subjects |
| Series | Student Mathematical Library ; v.104 Student mathematical library ; v. 104. ^A438915 |
| Contents | Preface -- Fundamental theorem of 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. |
| Abstract | 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. |
| Bibliography note | Includes bibliographical references and index. |
| Source of description | Description based on online resource; title from PDF title page (American Mathematical Society, viewed July 26, 2023). |
| Issued in other form | Print version: Murty, Maruti Ram. Introduction to the circle method. Providence, Rhode Island : American Mathematical Society, [2023] 9781470472030 |
| ISBN | 9781470474249 (electronic bk.) |
| ISBN | 1470474247 (electronic bk.) |