Counting Fields Generated by Polynomials of Given Height

Speaker:

Alina Ostafe

Affiliation:

U. New South Wales/MPIM

Date:

Mon, 19/12/2016 - 15:05 - 15:50

Location:

MPIM Lecture Hall [2]

Parent event:

Number theory lunch seminar [3]

We present a lower bound on the number of distinct fields generated by polynomials with integer coefficients fixed degree and growing height.

Our approach is based on a link between the discriminants of number fields and square free parts of the discriminants generating polynomials combined with the square-sieve of Heath-Brown.

This is joint work with Rainer Dietman and Igor Shparlinski.