Geodesic
A Note on Integer Symmetric Matrices and Mahler's Measure
Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 57-59

Voir la notice de l'article provenant de la source Cambridge University Press

We find a lower bound on the absolute value of the discriminant of the minimal polynomial of an integral symmetric matrix and apply this result to find a lower bound on Mahler's measure of related polynomials and to disprove a conjecture of D. Estes and R. Guralnick.
DOI : 10.4153/CMB-2008-007-9
Mots-clés : 11C20, 11R06, Integer matrices, Lehmer's problem, Mahler's measure 
Dobrowolski, Edward. A Note on Integer Symmetric Matrices and Mahler's Measure. Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 57-59. doi: 10.4153/CMB-2008-007-9
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[1] [1] Dobrowolski, E., On a question of Lehmer and the number of irreducible factors of a polynomial. Acta Arith. 34(1979), no. 4, 391–401. Google Scholar

[2] [2] Estes, D. and Guralnick, R., Minimal polynomials of integral symmetric matrices. Computational linear algebra in algebraic and related problems. Linear Algebra Appl. 192(1993), 83–89. Google Scholar

[3] [3] McKee, J. and Smyth, C. J. Salem numbers, Pisot numbers, Mahler measure and graphs. Experiment. Math. 14(2005), no. 2, 211–229. Google Scholar

[4] [4] Simon, D., Équations dans les corps de nombres et discriminants minimaux. Ph.D. thesis, Université Bordeaux-I, 1998. Google Scholar

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