Let theta = p/q with p and q relatively prime and u and v a pair of unitaries such that u v = e^{ i theta} v u, where u and v generate the rotation C*-algebra A_theta. Let h_{ theta, lambda} = u + u^{ -1} + lambda/2(v + v^{ -1}) be the almost Mathieu operator. By proving an identity of rational functions we show that for q even, the constant term in the characteristic polynomial of h_{ \theta, \lambda} is (-1)^{ q/2}(1 + (\lambda/2)^q) - (z_1^q + z_1^{ -q} + (\lambda/2)^q(z_2^q + z_2^{ -q})).
Categories: math.OA