On real and p-adic Bezoutians

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Title: On real and p-adic Bezoutians
Author: Adduci, Silvia María
Abstract: 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 .
URI: http : / /hdl .handle .net /2152 /ETD -UT -2010 -05 -998
Date: 2011-01-07

Citation

On real and p-adic Bezoutians. Doctoral dissertation, University of Texas at Austin. Available electronically from http : / /hdl .handle .net /2152 /ETD -UT -2010 -05 -998 .

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