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Composition of Binary Quadratic Forms

Understanding the Approaches of Gauss, Dirichlet and Bhargava

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Abstract

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

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Acknowledgment

I would like to thank Professor M. Ram Murty, Siddhi Pathak, as well as the referee for their helpful comments and suggestions on a previous version of this article.

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Authors and Affiliations

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

    François Séguin

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  1. François Séguin
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Correspondence to François Séguin.

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François Séguin received his PhD from Queen’s University in 2018. His research interests are in analytic number theory, specifically concerning questions of algebraic nature.

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Séguin, F. Composition of Binary Quadratic Forms. Reson 24, 633–651 (2019). https://doi.org/10.1007/s12045-019-0822-4

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  • DOI: https://doi.org/10.1007/s12045-019-0822-4

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