On real and p-adic Bezoutians

dc.contributor.advisorVillegas, Fernando Rodriguezen
dc.contributor.committeeMemberHelm, Daviden
dc.contributor.committeeMemberVaaler, Jeffreyen
dc.contributor.committeeMemberVoloch, Felipeen
dc.contributor.committeeMemberSturmfels, Bernden
dc.creatorAdduci, Silvia Maríaen
dc.date.accessioned2011-01-07T21:08:55Zen
dc.date.available2011-01-07T21:08:55Zen
dc.date.available2011-01-07T21:09:00Zen
dc.date.issued2010-05en
dc.date.submittedMay 2010en
dc.date.updated2011-01-07T21:09:00Zen
dc.descriptiontexten
dc.description.abstractWe study the quadratic form induced by the Bezoutian of two polynomials p and q, considering four problems. First, over R, in the separable case we count the number of configurations of real roots of p and q for which the Bezoutian has a fixed signature. Second, over Qp we develop a formula for the Hasse invariant of the Bezoutian. Third, we formulate a conjecture for the behavior of the Bezoutian in the non separable case, and offer a proof over R. We wrote a Pari code to test it over Qp and Q and found no counterexamples. Fourth, we state and prove a theorem that we hope will help prove the conjecture in the near future.en
dc.description.departmentMathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2010-05-998en
dc.language.isoengen
dc.subjectBezoutianen
dc.subjectp-adicen
dc.subjectInterlacingen
dc.subjectHasse invarianten
dc.titleOn real and p-adic Bezoutiansen
dc.type.genrethesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorUniversity of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen
Files
Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
ADDUCI-DISSERTATION.pdf
Size:
517.37 KB
Format:
Adobe Portable Document Format
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
2.12 KB
Format:
Plain Text
Description: