• Composition of Binary Quadratic Forms: Understanding the Approaches of Gauss, Dirichlet and Bhargava

    • Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/reso/024/06/0633-0651

    • Keywords

       

      Cubes of integers, binary quadratic forms, composition laws.

    • Abstract

       

      In 2004, Bhargava introduced a new way to understand thecomposition law of integral binary quadratic forms throughwhat he calls the ‘cubes of integers’. The goal of this articleis to introduce the reader to Bhargava’s cubes and this newcomposition law, as well as to relate it to the composition lawas it is known classically. We will present a historical expositionof the subject, from Gauss to Bhargava, and see howthe different formulations of the composition laws are equivalent.

    • Author Affiliations

       

      François S\'{e}guin1

      1. Department of Mathematics Queen’s University, Kingston Ontario K7L 3N6, Canada.
    • Dates

       

© 2021-2022 Indian Academy of Sciences, Bengaluru.