2021/03/29 by Celis, Monica, Almeida, Paulo
#11A51 #11E16 #FOS: Mathematics #History and Overview (math.HO)
paper · doi:10.48550/arxiv.2103.17036
In Disquisitiones Arithmeticae, Gauss studied binary quadratic forms and introduced a very general version of a composition operator that allows composing even forms of different discriminants and imprimitive forms. Section V of Disquisitiones contains truly revolutionary ideas and involves very complicated computations, sometimes left to the reader. With this theory, Gauss develops a method of factorization using quadratic residues obtained by binary quadratic forms. In this work we explore Gauss method making many of the computations necessary to better understand his work.