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It is known that the Lyapunov exponent for multifrequency analytic cocyclesis weak-H\"older continuous in cocycle for certain Diophantine frequencies, andthat this implies certain regularity of the integrated density of states inenergy for Jacobi operators. In this paper, we establish the pointwise modulusof continuity in both cocycle and frequency and obtain analogous regularity ofthe integrated density of states in energy, potential, and frequency.

Pointwise modulus of continuity of the Lyapunov exponent and integrated  density of states for analytic multi-frequency quasiperiodic $M(2,  \mathbb{C})$ cocycles