Resumen de Lattice points in rotated convex domains

Jingwei Guo

• If B⊂Rd (d⩾2) is a compact convex domain with a smooth boundary of finite type, we prove that for almost every rotation θ∈SO(d) the remainder of the lattice point problem, PθB(t), is of order Oθ(td−2+2/(d+1)−ζd) with a positive number ζd. Furthermore we extend the estimate of the above type, in the planar case, to general compact convex domains.