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.
| Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:cmc_theses-1862 |
| Date | 01 January 2014 |
| Creators | Shaughnessy, John F |
| Publisher | Scholarship @ Claremont |
| Source Sets | Claremont Colleges |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | CMC Senior Theses |
| Rights | © 2014 John F. Shaughnessy |
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