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Birkhäuser

Cubic Forms and the Circle Method

  • Book
  • © 2021

Overview

Authors:
  1. Tim Browning

    1. Institute of Science and Technology Austria, Klosterneuburg, Austria

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  • Gives a modern account of the Hardy–Littlewood circle method
  • Including its workings over number fields and function fields
  • Illustrates the use of the circle method in algebraic geometry

Part of the book series: Progress in Mathematics (PM, volume 343)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Cubic Forms Over Local Fields

    • Tim Browning
    Pages 1-24

  3. Waring’s Problem for Cubes

    • Tim Browning
    Pages 25-56

  4. Cubic Forms via Weyl Differencing

    • Tim Browning
    Pages 57-87

  5. Norm Forms Over Number Fields

    • Tim Browning
    Pages 89-112

  6. Diagonal Cubic Forms Over Function Fields

    • Tim Browning
    Pages 113-139

  7. Lines on Cubic Hypersurfaces

    • Tim Browning
    Pages 141-157

  8. Back Matter

    Pages 159-166
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Keywords

About this book

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.

Reviews

“It is recommended for readers with a solid background in abstract algebra, local fields, algebraic varieties and some analytic and algebraic number theory.” (Franz Lemmermeyer, zbMATH 1493.11003, 2022)

Authors and Affiliations

  • Institute of Science and Technology Austria, Klosterneuburg, Austria

    Tim Browning

About the author

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

Bibliographic Information

  • Book Title: Cubic Forms and the Circle Method

  • Authors: Tim Browning

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-86872-7

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-86871-0Published: 20 November 2021

  • Softcover ISBN: 978-3-030-86874-1Published: 21 November 2022

  • eBook ISBN: 978-3-030-86872-7Published: 19 November 2021

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: XIV, 166

  • Number of Illustrations: 2 illustrations in colour

  • Topics: Number Theory, Algebraic Geometry

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