Introduction to the Circle Method

Murty, M. Ram; Sinha, Kaneenika

ISBN 10: 1470472031 / ISBN 13: 9781470472030

Editore: American Mathematical Society, 2023

Codice articolo 46282356-n

Riassunto:

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.

Dati bibliografici

Titolo: Introduction to the Circle Method
Casa editrice: American Mathematical Society
Data di pubblicazione: 2023
Legatura: Brossura
Condizione: New