Date of Award

8-9-2014

Document Type

Open Access Dissertation

Department

Mathematics

First Advisor

Frank Thorne

Abstract

The study of fake real quadratic orders is fascinating as their class group structure is similiar to real quadratic fields. Statistical data strongly agree with the heuristics of Cohen and Lenstra of real quadratics with class number one. We will investigate why this holds true as well as explore other analogues to open conjecture on real quadratic fields, such as the Ankeny-Artin-Chowla Conjecture, and present various results that mark the similiarities between real quadratic fields and fake real quadratic orders. Fake real quadratics are defined by inverting an ideal above any prime p which is split in OK where K = Q(p D) is an imaginary quadratic field. v

Included in

Mathematics Commons

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