Date of Award
5-2008
Document Type
Thesis
Degree Name
Master of Science (MS)
Legacy Department
Mathematical Science
Committee Chair/Advisor
James, Kevin L
Committee Member
Calkin , Neil J
Committee Member
Maharaj , Hiren
Abstract
Let K be a degree n extension of Q, and let O_K be the ring of algebraic integers in K. Let x >= 2. Suppose we were to generate an ideal sequence by choosing ideals with norm at most x from O_K, independently and with uniform probability. How long would our sequence of ideals need to be before we obtain a subsequence whose terms have a product that is a square ideal in O_K? We show that the answer is about exp((2\ln(x)\ln\ln(x))^(1/2)).
Recommended Citation
Lafferty, Matt, "The Square Threshold Problem in Number Fields" (2008). All Theses. 376.
https://tigerprints.clemson.edu/all_theses/376