a1 Departments of Mathematics and Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
a2 Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60680, USA
A stationary phase method is developed for the asymptotic evaluation, as R → ∞, of oscillatory sums of the form
It is extended to multidimensional sums. Numerical comparisons demonstrate the accuracy of the asymptotic approximations. The results are applied to the practical estimation of the number of lattice points in large domains in 2.
(Received February 05 1993)