Nicolas Banks, University of Waterloo
Classification Results for Intersective Polynomials With No Integral Roots
In this thesis defence, we introduce strongly intersective polynomials - polynomials with no integer roots but with a root modulo every positive integer - of degree 5-10. These are fascinating objects which make contact with many areas of math, including permutation group theory, splitting behaviour of prime ideals in number fields, and Frobenius elements from class field theory.
In particular, we explain the computation of a list of possible Galois groups of such polynomials. We also discuss constraints on the splitting behaviour of ramified primes; in the process, we argue that intersectivity can be thought of as a property of a Galois number field, together with its set of subfields of specified degrees.
MC 5417 or Join on Teams