**Integer symmetric matrices of small spectral radius and small Mahler measure.** / McKee, James; Smyth, Chris.

Research output: Working paper

Published

In a previous paper we completely described cyclotomic matrices--integer
symmetric matrices of spectral radius at most 2. In this paper we find all
minimal noncyclotomic matrices. As a consequence, we are able to determine all
integer symmetric matrices of spectral radius at most 2.019, and to determine
all integer symmetric matrices whose Mahler measure is at most 1.3. In
particular we solve the strong version of Lehmer's problem for integer
symmetric matrices: all noncyclotomic matrices have Mahler measure at least
"Lehmer's number" 1.17628... .

Original language | English |
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Publication status | Published - 2 Jul 2009 |

ID: 54233