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Student Mathematical Library: Introduction to the Circle Method by M. Ram Murty and Kaneenika Sinha (2023, Trade Paperback)
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An Introduction to the Circle Method by M. Ram Murty, Kaneenika Sinha [Paperback]
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About this product
Product Identifiers
PublisherAmerican Mathematical Society
ISBN-101470472031
ISBN-139781470472030
eBay Product ID (ePID)11061231652
Product Key Features
Number of Pages257 Pages
LanguageEnglish
Publication NameIntroduction to the Circle Method
SubjectGeneral
Publication Year2023
TypeTextbook
AuthorM. Ram Murty, Kaneenika Sinha
Subject AreaMathematics
SeriesStudent Mathematical Library
FormatTrade Paperback
Dimensions
Item Height0.8 in
Item Weight6.2 Oz
Item Length8.5 in
Item Width5.5 in
Additional Product Features
LCCN2023-009446
TitleLeadingAn
Series Volume Number104
Table Of ContentIntroduction and overview Fundamental theorem for 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 Bibliography Index.
SynopsisThe 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. 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 ......, 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.
LC Classification NumberQA241.M853 2023
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