Open Access Senior Thesis
Bachelor of Arts
© 2014 John F. Shaughnessy
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.
Shaughnessy, John F., "Finding Zeros of Rational Quadratic Forms" (2014). CMC Senior Theses. 849.