A070178 Coefficients of Lehmer's polynomial.

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

Offset: 0

Author

N. J. A. Sloane, May 13 2002

Keywords

• sign
• easy
• fini
• full

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

Examples

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

References

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

Links

• 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).

Crossrefs

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