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Quadratic and Higher Degree Forms

  • Book
  • © 2013

Overview

Editors:
  1. Krishnaswami Alladi

    1. Department of Mathematics, University of Florida Department of Mathematics, Gainesville, USA

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  2. Manjul Bhargava

    1. Department of Mathematics, Princeton University, Princeton, USA

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  3. David Savitt

    1. Department of Mathematics, University of Arizona, Tucson, USA

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  4. Pham Huu Tiep

    1. Department of Mathematics, University of Arizona, Tuscon, USA

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  • Provides survey lectures, also accessible to non-experts
  • Introduction summarizes current research on quadratic and higher degree forms with a presentation of the necessary background material
  • Contains expositions on the latest advances on some famous mathematical problems
  • Includes supplementary material: sn.pub/extras

Part of the book series: Developments in Mathematics (DEVM, volume 31)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Toy Models for D. H. Lehmer’s Conjecture II

    • Eiichi Bannai, Tsuyoshi Miezaki
    Pages 1-27

  3. On Representation of an Integer by X 2 + Y 2 + Z 2 and the Modular Equations of Degree 3 and 5

    • Alexander Berkovich
    Pages 29-49

  4. Almost Universal Ternary Sums of Squares and Triangular Numbers

    • Wai Kiu Chan, Anna Haensch
    Pages 51-62

  5. Weighted Generating Functions for Type II Lattices and Codes

    • Noam D. Elkies, Scott Duke Kominers
    Pages 63-108

  6. Quadratic Forms and Automorphic Forms

    • Jonathan Hanke
    Pages 109-168

  7. Integral Positive Ternary Quadratic Forms

    • William C. Jagy
    Pages 169-179

  8. Some Aspects of the Algebraic Theory of Quadratic Forms

    • R. Parimala
    Pages 181-205

  9. On the Length of Binary Forms

    • Bruce Reznick
    Pages 207-232

  10. Representation of Quadratic Forms by Integral Quadratic Forms

    • Rainer Schulze-Pillot
    Pages 233-253

  11. Identifying the Matrix Ring: Algorithms for Quaternion Algebras and Quadratic Forms

    • John Voight
    Pages 255-298
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Keywords

About this book

In the last decade, the areas of quadratic and higher degree forms have witnessed dramatic advances. This volume is an outgrowth of three seminal conferences on these topics held in 2009, two at the University of Florida and one at the Arizona Winter School. The volume also includes papers from the two focused weeks on quadratic forms and integral lattices at the University of Florida in 2010.Topics discussed include the links between quadratic forms and automorphic forms, representation of integers and forms by quadratic forms, connections between quadratic forms and lattices, and algorithms for quaternion algebras and quadratic forms. The book will be of interest to graduate students and mathematicians wishing to study quadratic and higher degree forms, as well as to established researchers in these areas.

Quadratic and Higher Degree Forms contains research and semi-expository papers that stem from the presentations at conferences at the University of Florida as well as survey lectures on quadratic forms based on the instructional workshop for graduate students held at the Arizona Winter School. The survey papers in the volume provide an excellent introduction to various aspects of the theory of quadratic forms starting from the basic concepts and provide a glimpse of some of the exciting questions currently being investigated. The research and expository papers present the latest advances on quadratic and higher degree forms and their connections with various branches of mathematics.

Editors and Affiliations

  • Department of Mathematics, University of Florida Department of Mathematics, Gainesville, USA

    Krishnaswami Alladi

  • Department of Mathematics, Princeton University, Princeton, USA

    Manjul Bhargava

  • Department of Mathematics, University of Arizona, Tucson, USA

    David Savitt

  • Department of Mathematics, University of Arizona, Tuscon, USA

    Pham Huu Tiep

Bibliographic Information

  • Book Title: Quadratic and Higher Degree Forms

  • Editors: Krishnaswami Alladi, Manjul Bhargava, David Savitt, Pham Huu Tiep

  • Series Title: Developments in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4614-7488-3

  • Publisher: Springer New York, NY

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

  • Copyright Information: Springer Science+Business Media New York 2013

  • Hardcover ISBN: 978-1-4614-7487-6Published: 08 August 2013

  • Softcover ISBN: 978-1-4939-0144-9Published: 26 August 2015

  • eBook ISBN: 978-1-4614-7488-3Published: 13 August 2013

  • Series ISSN: 1389-2177

  • Series E-ISSN: 2197-795X

  • Edition Number: 1

  • Number of Pages: IX, 298

  • Topics: Number Theory, Combinatorics, Special Functions

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