Lattice points in large regions and related arithmetic functions: Recent developments in a very classic topic

Abstract

This is a survey article on the theory of lattice points in large planar domains and bodies of dimensions 3 and higher, with an emphasis on recent developments and new methods, including a lot of results established only during the last few years. It deals with the classic circle and sphere problems, as well as with the present state-of-the-art concerning lattice points in more general regions and bodies. Furthermore, a thorough account is given on divisor problems and related arithmetic functions.