Scheidler, RenateJacobson, Michael John Jr.Wang, Hongyan2017-01-122017-01-1220172017Wang, H. (2017). Numerical Tests of Two Conjectures in Fake Real Quadratic Orders (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/27146http://hdl.handle.net/11023/3560A fake real quadratic order is defined based on an imaginary quadratic field and a prime p but behaves similarly to real quadratic orders. Two conjectures regarding fake real quadratic orders are discussed in the thesis. The first one is the Cohen-Lenstra heuristic. Our computation showed that for fixed p, the proportion of fake real quadratic orders for which the odd part of the class number is one converges to C=0.754458..., which equals exactly the proportion of real quadratic fields for which the odd part of the class number is one. The second one is the Ankeny-Artin-Chowla conjecture, which states that D∤b where b is the second coefficient of the fundamental unit in the real quadratic field Q(√D). No counterexamples have been found in real quadratic fields but we found numerous counterexamples in fake real quadratic orders and this is evidence that the conjecture is false for real quadratic fields.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.Education--Mathematicsmaster thesis10.11575/PRISM/27146