Divisibility of Discriminants of Homogeneous Polynomials
| dc.contributor.author | Vukovic, Andrej | |
| dc.date.accessioned | 2023-08-28T14:00:33Z | |
| dc.date.available | 2023-08-28T14:00:33Z | |
| dc.date.issued | 2023-08-28 | |
| dc.date.submitted | 2023-08-23 | |
| dc.description.abstract | We prove several square-divisibility results about the discriminant of homogeneous polynomials of arbitrary degree and number of variables, when certain coefficients vanish, and give characterizations for when the discriminant is divisible by $p^2$ for $p$ prime. We also prove several formulas about a certain polynomial $\Delta_d'$, first introduced in (Bhargava, Shankar, Wang, 2022), which behaves like an average over the partial derivatives of $\Delta_d$, the discriminant of degree $d$ polynomials. In particular, we prove that $\Delta_d'$ is irreducible when $d\geq 5$. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/19767 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | mathematics | en |
| dc.subject | algebraic geometry | en |
| dc.subject | number theory | en |
| dc.title | Divisibility of Discriminants of Homogeneous Polynomials | en |
| dc.type | Doctoral Thesis | en |
| uws-etd.degree | Doctor of Philosophy | en |
| uws-etd.degree.department | Pure Mathematics | en |
| uws-etd.degree.discipline | Pure Mathematics | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws-etd.embargo.terms | 0 | en |
| uws.contributor.advisor | Wang, Jerry Xiaoheng | |
| uws.contributor.advisor | McKinnon, David | |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |