For an arbitrary irrational angle \alpha and arbitrary coupling constant \lambda, the Lebesgue measure of the spectrum of the Almost Mathieu operator with these parameters is equal to 4 |1-\lambda|. This was first conjectured in works by S. Aubry and G. Andre (1980), and later established in a series of results by J. Avron, P. H. M. v. Mouche & B. Simon (1990), Jitomirskaya and Last (1998), Jitomirskaya and Krasovsky (2001), Avila and Krikorian (2006).
     The main result of this talk, that is a work in progress with Anton Gorodetski, is devoted to the answer to the following question: what can be said about the measure of the part of the spectrum that is comprised between two given gaps? We show that the dependence on the parameters is piecewise-analytic: it is analytic on any domain when the bounding gaps do not bifurcate. We also show that the moments of the Lebesgue measure, restricted on the spectrum, are polynomials in \lambda and trigonometric polynomials in \alpha.