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
Rights
© 2014, Richard Michael Oh
Recommended Citation
Oh, R. M.(2014). Fake Real Quadratic Orders. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/2875