Finding Zeros of Rational Quadratic Forms

Author

John F. Shaughnessy, Claremont McKenna CollegeFollow

Graduation Year

Spring 2014

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Reader 1

Lenny Fukshansky

Reader 2

David Krumm

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Rights Information

© 2014 John F. Shaughnessy

Abstract

In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski Theorem that allows us to use p-adic analysis determine whether a quadratic form has a rational root. We then discuss search bounds and state Cassels' Theorem for small-height zeros of rational quadratic forms. We end with a proof of Cassels' Theorem and suggestions for further reading.

Comments

• Best Senior Thesis in Mathematics

Recommended Citation

Shaughnessy, John F., "Finding Zeros of Rational Quadratic Forms" (2014). CMC Senior Theses. 849.
https://scholarship.claremont.edu/cmc_theses/849