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An Introduction to the Circle Method: (Student Mathematical Library)

An Introduction to the Circle Method: (Student Mathematical Library)

          
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About the Book

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.

Table of Contents:
Introduction 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.


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Product Details
  • ISBN-13: 9781470472030
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Height: 216 mm
  • No of Pages: 257
  • Spine Width: 20 mm
  • Weight: 176 gr
  • ISBN-10: 1470472031
  • Publisher Date: 31 Aug 2023
  • Binding: Paperback
  • Language: English
  • Series Title: Student Mathematical Library
  • Volume: 104
  • Width: 140 mm


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