Cubic Forms and the Circle Method

The Hardy–Littlewood circle method is a powerful tool for studying integer solutions to Diophantine equations and rational curves on algebraic varieties, and this book is aimed at beginning graduate students. It has won the 2021 Ferran Sunyer i Balaguer Prize.

Format: Paperback / softback
Length: 166 pages
Publication date: 21 November 2022
Publisher: Springer Nature Switzerland AG

The Hardy–Littlewood circle method, a groundbreaking technique developed over a century ago, has emerged as a remarkably versatile tool in the field of number theory. Initially conceived to study integer solutions to special Diophantine equations, it has since proven to be an invaluable resource for number theorists across various domains. Not only does it possess the capability to handle remarkably general systems of polynomial equations defined over arbitrary global fields, but it also provides insights into the study of rational curves that lie on algebraic varieties.

In this comprehensive book, the arithmetic of cubic polynomials takes center stage, aimed at introducing beginning graduate students to the diverse aspects of the circle method, both classical and modern. The authors have designed this monograph to provide a solid foundation for those embarking on their journey into the world of number theory.

What sets this book apart is its prestigious recognition. It has been awarded the 2021 Ferran Sunyer i Balaguer Prize, a highly esteemed award for books of expository nature that present the latest developments in an active area of research in mathematics. This accolade serves as a testament to the significance and impact of the work presented within its pages.

The Hardy–Littlewood circle method has revolutionized the study of integer solutions to Diophantine equations, paving the way for further exploration in number theory and its applications. This book serves as a valuable resource for students, researchers, and enthusiasts alike, offering a comprehensive and up-to-date introduction to this powerful tool. Whether you are a novice or an experienced number theorist, this monograph will undoubtedly enhance your understanding and appreciation of the field.

Weight: 285g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030868741
Edition number: 1st ed. 2021