Event Type:

Number Theory Seminar

Date/Time:

Tuesday, November 21, 2017 - 16:15 to 17:15

Location:

Kidder 350

Guest Speaker:

Institution:

California State University, Chico

Abstract:

PLEASE NOTE THE CHANGE IN TIME AND THE CHANGE IN ROOM.

Abstract: The class number is among the most important invariants associated to a number field. The genus number is, in some sense, the part of the class number that is easier to understand. It is very natural to ask about the density of genus number one fields among all number fields of a fixed degree. We will discuss a recent result, joint with Amanda Tucker, on the density of genus number one cubic fields. Two different perspectives on the local density calculation at the prime 3 will be given. One of these perspectives allows us to carry out the analogous calculation in the quintic case in a straightforward manner. We will discuss this calculation if time permits.