On real and p-adic Bezoutians
We 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...
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2011
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| Online Access: | http://hdl.handle.net/2152/ETD-UT-2010-05-998 |
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ndltd-UTEXAS-oai-repositories.lib.utexas.edu-2152-ETD-UT-2010-05-9982015-09-20T16:56:50ZOn real and p-adic BezoutiansAdduci, Silvia MaríaBezoutianp-adicInterlacingHasse invariantWe 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.text2011-01-07T21:08:55Z2011-01-07T21:09:00Z2011-01-07T21:08:55Z2011-01-07T21:09:00Z2010-052011-01-07May 20102011-01-07T21:09:00Zthesisapplication/pdfhttp://hdl.handle.net/2152/ETD-UT-2010-05-998eng |
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NDLTD |
| language |
English |
| format |
Others
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| sources |
NDLTD |
| topic |
Bezoutian p-adic Interlacing Hasse invariant |
| spellingShingle |
Bezoutian p-adic Interlacing Hasse invariant Adduci, Silvia María On real and p-adic Bezoutians |
| description |
We 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. === text |
| author |
Adduci, Silvia María |
| author_facet |
Adduci, Silvia María |
| author_sort |
Adduci, Silvia María |
| title |
On real and p-adic Bezoutians |
| title_short |
On real and p-adic Bezoutians |
| title_full |
On real and p-adic Bezoutians |
| title_fullStr |
On real and p-adic Bezoutians |
| title_full_unstemmed |
On real and p-adic Bezoutians |
| title_sort |
on real and p-adic bezoutians |
| publishDate |
2011 |
| url |
http://hdl.handle.net/2152/ETD-UT-2010-05-998 |
| work_keys_str_mv |
AT adducisilviamaria onrealandpadicbezoutians |
| _version_ |
1716821129885122560 |