Lists of Polynomials with Small Mahler Measure

Complete List to Degree 44

The complete list of irreducible, noncyclotomic polynomials having degree at most 44 and Mahler measure below 1.3.

Known Polynomials Through Degree 72

All known irreducible, noncyclotomic polynomials with degree at most 72 and Mahler measure below 1.3 (143K html). This list is known to be complete through degree 44, and in addition, the smallest measure listed for each degree is known to be the minimal nontrivial measure for an algebraic number of this degree up to degree 54.

Known Polynomials Through Degree 180

All known irreducible, noncyclotomic polynomials with degree at most 180 and Mahler measure less than 1.3 (125K gzip'd text). This includes 42 new polynomials with degree at least 174 found by Petr Lisonek in January 2000, 19 additional polynomials with degree at least 174 found by Georges Rhin and Jean-Marc Sac-Epée in 2003, and three more polynomials (one each of degrees 46, 48, and 52), found by Rhin, Mossinghoff, and Wu in 2008.

Small Salem Numbers

All known Salem numbers less than 1.3. This list is known to be complete through degree 44.

More Salem Numbers

Complete lists of Salem numbers with fixed degree, up to the indicated bound, M.

• Degree 4, M = 3.
• Degree 6, M = 2.8.
• Degree 8, M = 2.6.
• Degree 10, M = 2.4.
• Degree 12, M = 2.2.
• Degree 14, M = 2.
• Degree 16, M = 1.8.
• Degree 18, M = golden ratio.
• Degree 20, M = golden ratio.
• Degree 22, M = 1.5.
• Degree 24, M = 1.4.

An explanation of the format used in the tables.

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