2004/10/25 by A. Ivic, E. Krätzel, Ivic, A. +5 · 3 citations
Mathematics · #11P21 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11P21
paper · pdf · doi:10.48550/arxiv.math/0410522
39 pages
arxiv created 2004/10/25 · arxiv updated 2009/12/01
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.