Advanced search
Publication Cover
Experimental Mathematics Volume 14, 2005 - Issue 4
Submit an article Journal homepage
27
Views
13
CrossRef citations to date
0
Altmetric
Original Article

Small Limit Points of Mahler's Measure

David W. Boyd Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1Z2, Canada
&
Michael J. Mossinghoff Department of Mathematics, Davidson College, Davidson, North Carolina 28035-6996
Pages 403-414 | Published online: 30 Jan 2011

  • C. Batut, K. Belabas, D. Bernardi, H. Cohen, and M. Olivier. "User's Guide to PARI/GP." Available from World Wide Web (http://pari.math .u-bordeaux.fr), 2000. http://pari.math.u-bordeaux.fr
  • M. J. Bertin. "Mesure de Mahler d'hypersurfaces K3." 2005. ArXiv:math.NT/0501153.
  • D. W. Boyd. "Small Salem Numbers." Duke Math. J. 44:2 (1977), 315–328.
  • D. W. Boyd. "Reciprocal Polynomials Having Small Measure." Math. Comp. 35:152 (1980), 1361–1377.
  • D. W. Boyd. "Kronecker's Theorem and Lehmer's Problem for Polynomials in Several Variables." J. Number Theory 13:1 (1981), 116–121.
  • D.W. Boyd. "Speculations Concerning the Range of Mahler's Measure." Canad. Math. Bull. 24:4 (1981), 453–469.
  • D. W. Boyd. "Reciprocal Polynomials Having Small Measure. II." Math. Comp. 53:187 (1989), 355–357, S1–S5.
  • D. W. Boyd. "Mahler's Measure and Special Values of L-Functions." Experiment. Math. 7:1 (1998), 37–82.
  • D. W. Boyd. "Uniform Approximation to Mahler's Measure in Several Variables." Canad. Math. Bull. 41:1 (1998), 125–128.
  • D. W. Boyd. "Mahler's Measure and Invariants of Hyperbolic Manifolds." In Number Theory for the Millennium, I (Urbana, IL, 2000),pp. 127–143. Natick, MA: A K Peters, 2002.
  • D. W. Boyd and F. Rodriguez Villegas. "Mahler's Measure and the Dilogarithm. I." Canad. J. Math. 54:3 (2002), 468–492.
  • R. Breusch. "On the Distribution of the Roots of a Polynomial with Integral Coefficients." Proc. Amer. Math. Soc. 2:6 (1951), 939–941.
  • C. Deninger. "Deligne Periods of Mixed Motives, K-Theory and the Entropy of Certain Zn- Actions." J. Amer. Math. Soc. 10:2 (1997), 259–281.
  • V. Flammang, G. Rhin, and J. -M. Sac- Épée. "Integer Transfinite Diameter and Polynomials with Small Mahler Measure." To appear in Math. Comp., 2006.
  • W. M. Lawton. "A Problem of Boyd Concerning Geometric Means of Polynomials." J. Number Theory 16:3 (1983), 356–362.
  • D. H. Lehmer. "Factorization of Certain Cyclotomic Functions." Ann. of Math. (2) 34:3 (1933), 461–479.
  • K. Mahler. "On Some Inequalities for Polynomials in Several Variables." J. London Math. Soc. 37 (1962), 341–344.
  • M. J. Mossinghoff. "Polynomials with Small Mahler Measure." Math. Comp. 67:224 (1998), 1697– 1705, S11–S14.
  • M. J. Mossinghoff. "Lehmer's Problem." Available from World Wide Web (http://www.cecm.sfu .ca/~mjm/Lehmer), 2004. http://www.cecm.sfu.ca/~mjm/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.
  • G. Rhin and J. -M. Sac-Épée. "New Methods Providing High Degree Polynomials with Small Mahler Measure." Experiment. Math. 12:4 (2003), 457–461.
  • F. Rodriguez Villegas. "Modular Mahler Measures. I." In Topics in Number Theory (University Park, PA, 1997), 17–48,pp Math. Appl. 467. Dordrecht: Kluwer Acad. Publ., 1999.
  • R. Salem. "Power Series with Integral Coefficients." Duke Math. J. 12 (1945), 153–172.
  • A. Schinzel. Polynomials with Special Regard to Reducibility, Encyclopedia Math. Appl., 77. Cambridge, UK: Cambridge Univ. Press, 2000.
  • C. L. Siegel. "Algebraic Integers whose Conjugates Lie in the Unit Circle." Duke Math. J. 11 (1944), 597–602.
  • 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.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.