## All Theses

#### Title

The Square Threshold Problem in Number Fields

5-2008

Thesis

#### Degree Name

Master of Science (MS)

#### Legacy Department

Mathematical Science

James, Kevin L

Calkin , Neil J

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)).

COinS