Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Entire DC Network
Explicit Composition Identities For Higher Composition Laws In The Quadratic Case, Ajith A. Nair
Explicit Composition Identities For Higher Composition Laws In The Quadratic Case, Ajith A. Nair
Dissertations, Theses, and Capstone Projects
The theory of Gauss composition of integer binary quadratic forms provides a very useful way to compute the structure of ideal class groups in quadratic number fields. In addition to that, Gauss composition is also important in the problem of representations of integers by binary quadratic forms. In 2001, Bhargava discovered a new approach to Gauss composition which uses 2x2x2 integer cubes, and he proved a composition law for such cubes. Furthermore, from the higher composition law on cubes, he derived four new higher composition laws on the following spaces - 1) binary cubic forms, 2) pairs of binary quadratic …
Arithmetic Of Binary Cubic Forms, Gennady Yassiyevich
Arithmetic Of Binary Cubic Forms, Gennady Yassiyevich
Dissertations, Theses, and Capstone Projects
The goal of the thesis is to establish composition laws for binary cubic forms. We will describe both the rational law and the integral law. The rational law of composition is easier to describe. Under certain conditions, which will be stated in the thesis, the integral law of composition will follow from the rational law. The end result is a new way of looking at the law of composition for integral binary cubic forms.