European Journal of Applied Mathematics

Research Article

Asymptotic evaluation of oscillatory sums

Joseph B. Kellera1 and Charles Knessla2

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)