- F. Amoroso and R. Dvornicich. "A Lower Bound for the Height in Abelian Extensions." J. Number Theory 80:2 (2000), 260-272.
- C. Batut, K. Belabas, D. Bernardi, H. Cohen, and M. Olivier. "GP-PARI," version 2.1.5, 2002.
- E. Bombieri and J. D. Vaaler. "Polynomials with Low Height and Prescribed Vanishing." In Analytic Number Theory and Diophantine Problems, edited by A. C. Adolphson et al., pp. 53-73, Progress in Mathematics 70. Cambridge: Birkhäuser, 1987.
- E. Bombieri and U. Zannier. "A Note on Heights in Certain Infinite Extensions of ℚ." Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 12 (2001), 5-14.
- P. Borwein. Computational Excursions in Analysis and Number Theory, CMS Books Math./Ouvrages Math SMC 10. New York: Springer, 2002.
- P. Borwein and T. Erdélyi. "The Integer Chebyshev Problem." Math. Comp. 65:214 (1996), 661-681.
- P. Borwein, E. Dobrowolski, and M. J. Mossinghoff. "Lehmer's Problem for Polynomials with Odd Coefficients." Ann. of Math. (2) 166:2 (2007), 347-366.
- D. W. Boyd. "Reciprocal Polynomials Having Small Measure." Math. Comp. 35:152 (1980), 1361-1377.
- D. W. Boyd. "Reciprocal Polynomials Having Small Measure, II." Math. Comp. 53:187 (1989), 355-357, S1-S5.
- D. W. Boyd, M. J. Mossinghoff. "Small Limit Points of Mahler's Measure." Experiment. Math. 14:4 (2005), 403-414.
- R. Breusch. "On the Distribution of the Roots of a Polynomial with Integral Coefficients." Proc. Amer. Math. Soc. 2:6 (1951), 939-941.
- E. Dobrowolski. "On a Question of Lehmer and the Number of Irreducible Factors of a Polynomial." Acta Arith. 34:4 (1979), 391-401.
- A. Dubickas and M. J. Mossinghoff. "Auxiliary Polynomials for Some Problems Regarding Mahler's Measure." Acta Arith. 119:1 (2005), 65-79.
- G. Everest and T. Ward. Heights of Polynomials and Entropy in Algebraic Dynamics, Universitext. London: Springer, 1999.
- V. Flammang, G. Rhin, and C. J. Smyth. "The Integer Transfinite Diameter of Intervals and Totally Real Algebraic Integers." J. Théor. Nombres Bordeaux 9:1 (1997), 137-168.
- V. Flammang, M. Grandcolas, and G. Rhin. "Small Salem Numbers." In Number Theory in Progress (Zakopane-Kościelisko, 1997), vol. 1, edited by A. Schinzel et al., pp. 165-168. Berlin: de Gruyter, 1999.
- V. Flammang, G. Rhin, and J.-M. Sac-Épée. "Integer Transfinite Diameter and Polynomials with Small Mahler Measure." Math. Comp. 75:255 (2006), 1527-1540.
- J. Garza. "The Mahler Measure of Dihedral Extensions." Acta Arith. 131:3 (2008), 201-215.
- E. Ghate and E. Hironaka. "The Arithmetic and Geometry of Salem Numbers." Bull. Amer. Math. Soc. (N.S.) 38:3 (2001), 293-314.
- E. Hironaka. "The Lehmer Polynomial and Pretzel Links." Canad. Math. Bull. 44:4 (2001), 440-451. Correction, ibid. 45:2 (2002), 231.
- E. Hironaka. "Lehmer's Problem, McKay's Correspondence, and 2, 3, 7." In Topics in Algebraic and Noncommutative Geometry (Luminy/Annapolis, MD, 2001), edited by C. G. Melles et al., pp. 123-138, Contemp. Math. 324. Providence: Amer. Math. Soc., 2003.
- G. Höhn and N.-P. Skoruppa. "Un résultat de Schinzel." J. ThÉor. Nombres Bordeaux 5:1 (1993), 185.
- D. H. Lehmer. "Factorization of Certain Cyclotomic Functions." Ann. of Math. (2) 34:3 (1933), 461-479.
- P. Lisonek. Private communication, 2000.
- M. Marden. Geometry of Polynomials. Providence: Amer. Math. Soc., 1966.
- C. T. McMullen. "Coxeter Groups, Salem Numbers and the Hilbert Metric." Publ. Math. Inst. Hautes Études Sci. 95 (2002), 151-183.
- M. J. Mossinghoff. "Polynomials with Small Mahler Measure." Math. Comp. 67:224 (1998), 1697-1705, S11-S14.
- M. J. Mossinghoff. "Polynomials with Restricted Coefficients and Prescribed Noncyclotomic Factors." LMS J. Comput. Math. 6 (2003), 314-325.
- M. J. Mossinghoff. "Lehmer's Problem." Available online ( http://www.cecm.sfu.ca/εmjm/ Lehmer
- M. J. Mossinghoff, C. G. Pinner, and J. D. Vaaler. "Perturbing Polynomials with All Their Roots on the Unit Circle." Math. Comp. 67:224 (1998), 1707-1726.
- I. E. Pritsker. "Small Polynomials with Integer Coefficients." J. Anal. Math. 96 (2005), 151-190.
- G. Rhin and J.-M. Sac-Épée. "New Methods Providing High Degree Polynomials with Small Mahler Measure." Experiment. Math. 12:4 (2003), 457-461.
- A. Schinzel. "On the Product of the Conjugates outside the Unit Circle of an Algebraic Number." Acta Arith. 24 (1973), 385-399. Addendum, ibid. 26 (1975), 329-331.
- A. Schinzel. Polynomials with Special Regard to Reducibility, Encyclopedia Math. Appl. 77. Cambridge: Cambridge Univ. Press, 2000.
- K. Schmidt. Dynamical Systems of Algebraic Origin, Progr. Math. 128. Basel: Birkhäuser, 1995.
- D. S. Silver and S. G. Williams. "Mahler Measure of Alexander Polynomials." J. London Math. Soc. (2) 69:3 (2004), 767-782.
- C. J. Smyth. "On the Product of the Conjugates outside the Unit Circle of an Algebraic Integer." Bull. London Math. Soc. 3 (1971), 169-175.
- C. J. Smyth. "The Mean Values of Totally Real Algebraic Integers." Math. Comp. 42:166 (1984), 663-681.
- C. J. Smyth. "The Mahler Measure of Algebraic Numbers: A Survey." In Number Theory and Polynomials, edited by J. McKee and C. Smyth, pp. 322-349, London Math. Society Lecture Note Series 352. Cambridge, UK: Cambridge University Press, 2008.
- P. Voutier. "An Effective Lower Bound for the Height of Algebraic Numbers." Acta Arith. 74:1 (1996), 81-95.
- M. Waldschmidt. Diophantine Approximation on Linear Algebraic Groups, Grundlehren Math. Wiss. 326. Berlin: Springer, 2000.
- Q. Wu. "On the Linear Independence Measure of Logarithms of Rational Numbers." Math. Comp. 72:242 (2003), 901-911.
Minimal Mahler Measures
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