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1. Shepherd, Rick L. Binary quadratic forms and genus theory.

Degree: 2013, University of North Carolina – Greensboro

URL: http://libres.uncg.edu/ir/listing.aspx?styp=ti&id=15057

The study of binary quadratic forms arose as a natural
generalization of questions about the integers posed by the ancient
Greeks. A major milestone of understanding occurred with the
publication of Gauss's Disquisitiones
Arithmeticae in 1801 in which Gauss systematically
treated known results of his predecessors and vastly increased
knowledge of this part of number theory. In effect, he showed how
collections of sets of binary quadratic forms can be viewed as
groups, at a time before group theory formally existed. Beyond
that, he even defined and calculated genus groups, which are
essentially quotient groups, that explain which congruence classes
of numbers can be represented by given sets of forms. This thesis
examines Gauss's main results as interpreted and refined over two
centuries. Also code has been created to implement many of the
algorithms used in studying the relationships of such forms to each
other, to generate examples, and to provide a small toolkit of
software for analyzing the corresponding algebraic structures.;
Binary quadratic forms, Class groups, Class number, Genus theory,
PARI code
*Advisors/Committee Members: Brett Tangedal (advisor).*

Subjects/Keywords: Forms, Binary; Forms, Quadratic; Group theory

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APA (6^{th} Edition):

Shepherd, R. L. (2013). Binary quadratic forms and genus theory. (Masters Thesis). University of North Carolina – Greensboro. Retrieved from http://libres.uncg.edu/ir/listing.aspx?styp=ti&id=15057

Chicago Manual of Style (16^{th} Edition):

Shepherd, Rick L. “Binary quadratic forms and genus theory.” 2013. Masters Thesis, University of North Carolina – Greensboro. Accessed July 15, 2020. http://libres.uncg.edu/ir/listing.aspx?styp=ti&id=15057.

MLA Handbook (7^{th} Edition):

Shepherd, Rick L. “Binary quadratic forms and genus theory.” 2013. Web. 15 Jul 2020.

Vancouver:

Shepherd RL. Binary quadratic forms and genus theory. [Internet] [Masters thesis]. University of North Carolina – Greensboro; 2013. [cited 2020 Jul 15]. Available from: http://libres.uncg.edu/ir/listing.aspx?styp=ti&id=15057.

Council of Science Editors:

Shepherd RL. Binary quadratic forms and genus theory. [Masters Thesis]. University of North Carolina – Greensboro; 2013. Available from: http://libres.uncg.edu/ir/listing.aspx?styp=ti&id=15057