Equidistribution on the Sphere

A concept of generalized discrepancy, which involves pseudodiierential operators to give a criterion of equidistributed pointsets, is developed on the sphere. A simply structured formula in terms of elementary functions is established for the computation of the generalized discrepancy. With the help of this formula ve kinds of point systems on the sphere, namely lattices in polar coordinates, transformed 2-dimensional sequences, rotations on the sphere, triangulation, and "sum of three squares sequence", are investigated. Quantitative tests are done, and the results are compared with each other. Our calculations exhibit diierent orders of convergence of the generalized discrepancy for diierent types of point systems.