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Coefficients of Lehmer's polynomial.
3

%I #21 Aug 18 2021 15:29:17

%S 1,1,0,-1,-1,-1,-1,-1,0,1,1

%N Coefficients of Lehmer's polynomial.

%C Mahler's measure M(f) of a polynomial f is defined to be the absolute value of the product of those roots of f which lie outside the unit disk, multiplied by the absolute value of the coefficient of the leading term of f. Of all polynomials with integer coefficients, Lehmer's 10th degree polynomial produces the smallest known M(f), given in A073011. - _Hugo Pfoertner_, Mar 12 2006

%D H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., 1996, p. 205.

%H D. H. Lehmer, <a href="http://www.jstor.org/stable/1968172">Factorization of certain cyclotomic functions</a>, Annals of Math. vol. 34, 1933, pp. 461-479.

%H Douglas Lind, <a href="https://arxiv.org/abs/math/0303279">Lehmer's Problem for compact abelian groups</a>, arXiv:math/0303279 [math.NT], 2003-2014.

%H Michael Mossinghoff, <a href="https://web.archive.org/web/20131027202648/http://oldweb.cecm.sfu.ca/~mjm/Lehmer/">Lehmer's Problem</a>.

%H Charles L. Samuels, <a href="http://arxiv.org/abs/1408.4165">The infimum in the metric Mahler measure</a>, arXiv:1408.4165 [math.NT], 2014 (see page 2).

%e Polynomial is 1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10.

%Y Cf. A073011 (Mahler's measure of Lehmer's polynomial).

%K sign,easy,fini,full

%O 0,1

%A _N. J. A. Sloane_, May 13 2002