Lehmer’s conjecture and the Fuglede-Kadison determinant

Lehmer’s conjecture is one of the most striking open problems in number theory. It roughly postulates that the complex roots $$a$$ with $$|a| > 1$$ of a polynomial with integral coefficients cannot simultaneously be close to the unit circle (unless all non-zero roots lie on the unit circle). More precisely, the Mahler measure of a … Continue reading "Lehmer’s conjecture and the Fuglede-Kadison determinant"