  In this paper, we establish quantitative Green's function estimates for some
higher dimensional lattice quasi-periodic (QP) Schr\"odinger operators. The
resonances in the estimates can be described via a pair of symmetric zeros of
certain functions and the estimates apply to the sub-exponential type
non-resonant conditions. As the application of quantitative Green's function
estimates, we prove both the arithmetic version of Anderson localization and
the $(\frac 12-)$-H\"older continuity of the integrated density of states (IDS)
for such QP Schr\"odinger operators. This gives an affirmative answer to
Bourgain's problem in\cite{Bou00}.
