Cubic Forms and the Circle Method

1. Auflage 2021
ISBN: 978-3-030-86874-1
Verlag: Springer International Publishing

Buch, Englisch, Band 343, 166 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 283 g

Reihe: Progress in Mathematics

The Hardy–Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists. Not only is it capable of handling remarkably general systems of polynomial equations defined over arbitrary global fields, but it can also shed light on the space of rational curves that lie on algebraic varieties. This book, in which the arithmetic of cubic polynomials takes centre stage, is aimed at bringing beginning graduate students into contact with some of the many facets of the circle method, both classical and modern. This monograph is the winner of the 2021 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.

Zielgruppe

Research

Autoren/Hrsg.

Browning, Tim

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

- 1. Cubic Forms Over Local Fields. - 2. Waring’s Problem for Cubes. - 3. Cubic Forms via Weyl Differencing. - 4. Norm Forms Over Number Fields. - 5. Diagonal Cubic Forms Over Function Fields. - 6. Lines on Cubic Hypersurfaces.

Über Autor(innen)

Tim Browning is a professor of number theory with a focus on analytic number theory and Diophantine geometry.