A070178 Coefficients of Lehmer's polynomial.

1, 1, 0, -1, -1, -1, -1, -1, 0, 1, 1

Offset

0,1

Comments

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

References

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

Links

Table of n, a(n) for n=0..10.

D. H. Lehmer, Factorization of certain cyclotomic functions, Annals of Math. vol. 34, 1933, pp. 461-479.

Douglas Lind, Lehmer's Problem for compact abelian groups, arXiv:math/0303279 [math.NT], 2003-2014.

Michael Mossinghoff, Lehmer's Problem.

Charles L. Samuels, The infimum in the metric Mahler measure, arXiv:1408.4165 [math.NT], 2014 (see page 2).

Example

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

Crossrefs

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

Sequence in context: A040051 A108788 A103583 * A364250 A289748 A127254

Adjacent sequences: A070175 A070176 A070177 * A070179 A070180 A070181

Keyword

sign,easy,fini,full

Author

N. J. A. Sloane, May 13 2002

Status

approved