An introduction to the circle method

Author(s)

Bibliographic Information

An introduction to the circle method

M.Ram Murty, Kaneenika Sinha

(Student mathematical library, v. 104)

American Mathematical Society, c2023

  • : pbk

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Note

Includes bibliographical references (p. 249-253) and index

Description and Table of Contents

Description

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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Details

  • NCID
    BD02885243
  • ISBN
    • 9781470472030
  • Country Code
    us
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Providence, R.I.
  • Pages/Volumes
    xix, 257 p.
  • Size
    22 cm
  • Parent Bibliography ID
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