Student Number Theory Seminar

Nolan Pyott, Department of Pure Mathematics, University of Waterloo

"Counting Irreducible Polynomials with the Turán Sieve"

Irreducible polynomials are an important aspect of understanding polynomials and the main application in this presentation will be to determine a density of irreducible monic polynomials over the integers. To begin, we will first explore the case of quadratic polynomials over the integers and then the issues with counting higher order irreducible polynomials. This will motivate the Turán sieve which can then be used to complete the proof for higher degree polynomials. After the application, a proof is given of the sieve inequality itself. To demonstrate the sieve again, it is briefly applied to counting the square values of polynomials.

Place: gather.town Graduate space, the middle bottom whiteboard, link: https://app.gather.town/app/S1fgkHgk7P3dUDtw/graduate