Summary of Small Mahler Measures

For each degree D up to 72, this table shows the number of known primitive, irreducible, noncyclotomic polynomials with degree D and Mahler measure less than 1.3 having exactly k roots outside the unit circle. The columns of the table correspond to the different values of k.

Deg     1   2   3   4   5   6   7   8   9  10  11  12  13  Total
 8      1                                                      1
10      5   2                                                  7
12      1   4                                                  5
14      4   5   2                                             11
16      1  12       1                                         14
18      7   8   8                                             23
20      4  22   3   6                                         35
22      4  12  27   4   1                                     48
24      2  29   3  11       1                                 46
26      7  11  21  11  11                                     61
28      1  15  14  28   1                                     59
30      4  10  36  20   8   2                                 80
32         12   8  35   7   7                                 69
34      2   5  24  19  30   8   2                             90
36      1  15  11  36   4  20       1                         88
38          1  18  18  29   8  12                             86
40      1   9   7  32  10  23   2   3                         87
42             11  14  16   6   8   2                         57
44      1   2   4  29   5  25   4   7                         77
46      1   1  10  13  37  11  23   7   3                    106
48          2   4  24   4  25   1  19   1                     80
50              4  10  15  14  16   9   8                     76
52              2   7   8  21   4  17   4   3                 66
54                  4  14  15  14   3  15   1                 66
56                  6   5  16   7  11   4   6                 55
58              3   1  15  12  21   9  25   9   4             99
60              2   5   4  19   4  13      18                 65
62              1      10  12  20   7  19   9  13             91
64                  7   2   8   6  17   5  16   5   3         69
66              1       5   5  11  11   7       6             46
68              1   1   2  11  11  12   3  12   5  10         68
70                      7   9  24  16  21   7  26   7   5    122
72                  1   1  10   2  18       8      17         57
Total  47 177 225 343 251 288 192 182 115  89  59  37   5   2010

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Last modified June 5, 2009