Mahler's Measure of a Polynomial in Function of the Number of its Coefficients
Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 186-195

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

Mahler's measure of a monic polynomial is equal to the product of modules of its roots which lie outside the unit circle. By classical theorem of Kronecker it is strictly greater than 1 for any polynomial that is not a product of cyclotomic factors. In this case a number of lower bounds of the measure, depending either on the degree of the polynomial or on the number of its non-zero coefficients, has been found. Here is given an improvement of the bound of the latter type previously found by the author, A. Schinzel and W. Lawton.
DOI : 10.4153/CMB-1991-030-5
Mots-clés : 11R04, 11R09, 11C08.
Dobrowolski, Edward. Mahler's Measure of a Polynomial in Function of the Number of its Coefficients. Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 186-195. doi: 10.4153/CMB-1991-030-5
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[1] 1. Cassels, J. W. S., An Introduction to the Geometry of Numbers, Springer Verlag, Berlin, Gottingen, Heidelberg 1959. Google Scholar

[2] 2. Dobrowolski, E., On a question of Lehmer and the number of irreducible factors of a polynomial, Acta Arith., 34 (1979), 391–401. Google Scholar

[3] 3. Dobrowolski, E., Lawton, W., Schinzel, A., On a problem of Lehmer, Studies in Pure Mathematics, 135–144, Birkàuser, Basel — Boston, Mass., 1983. Google Scholar

[4] 4. Montgomery, H. L. and Schinzel, A., Some arithmetic properties of polynomials in several variables, pp. 195-203 in Transcendence Theory; Advances and Applications, London — New York — San Francisco 1977. Google Scholar

[5] 5. Lehmer, D. H., Factorization of certain cyclotomic functions, Ann. Math., (2), 34 (1933), 461-479. Google Scholar

[6] 6. Smyth, C. J., On the product of conjugates outside the unit circle of an algebraic integer, Bull. London Math. Soc.3(1971), 169–175. Google Scholar

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