Abstract
We consider the generating function of the algebraic area of lattice walks, evaluated at a root of unity, and its relation to the Hofstadter model. In particular, we obtain an expression for the generating function of the nth moments of the Hofstadter Hamiltonian in terms of a complete elliptic integral, evaluated at a rational function. This, in turn, gives us both exact and asymptotic formulas for these moments.
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