Abstract

In \(\mathbb{Q}(i),\) the elements of norm 1 correspond to rational points on the unit circle. In a quadratic number field, this generalizes to rational points on an ellipse. We'll discuss the geometry of the norm 1 elements in any number field, and formulate the equidistribution problem. If time allows, we'll discuss the proof of equidistribution in the cyclic case, and the difficulty in the general case.