Title: Lattice Point Problems and the Central Limit Theorem in Euclidean Spaces

A number of problems in probability and statistics lead to questions about the actual error in the asymptotic approximation of nonlinear functions of the observations. Recently new methods have emerged which provide optimal bounds for statistics of quadratic type. These tools are adaptions of methods which provide sharp bounds in some high dimensional lattice point remainder problems and solve some problems concerning the distribution of values of quadratic forms.

1991 Mathematics Subject Classification: Primary 62E20, 11P21 Secondary 60F05

Keywords and Phrases: Edgeworth expansion, $U$-statistics, Central Limit Theorem, lattice point rest, ellipsoids, irrational quadratic forms

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