  In this work we prove the weighted Gevrey regularity of solutions to the
incompressible Euler equation with initial data decaying polynomially at
infinity. This is motivated by the well-posedness problem of vertical boundary
layer equation for fast rotating fluid. The method presented here is based on
the basic weighted $L^2$- estimate, and the main difficulty arises from the
estimate on the pressure term due to the appearance of weight function.
