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We prove the H\"older continuity of the integrated density of states for aclass of quasi-periodic long-range operators on $\ell^2(\Z^d)$ with largetrigonometric polynomial potentials and Diophantine frequencies. Moreover, wegive the H\"older exponent in terms of the cardinality of the level sets of thepotentials, which improves, in the perturbative regime, the result obtained byGoldstein and Schlag \cite{gs2}. Our approach is a combination of Aubryduality, generalized Thouless formula and the regularity of the Lyapunovexponents of analytic quasi-periodic $GL(m,\C)$ cocycles which is proved byquantitative almost reducibility method.

H\"older regularity of the integrated density of states for quasi-periodic long-range operators on $\ell^2(\Z^d)$