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Asymptotic evaluation of oscillatory sums

Published online by Cambridge University Press:  26 September 2008

Joseph B. Keller  and
Charles Knessl
Joseph B. Keller
Affiliation:
Departments of Mathematics and Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Charles Knessl
Affiliation:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL 60680, USA
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Abstract

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 ℝ2.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 4 , Issue 4 , December 1993 , pp. 361 - 379
Copyright
Copyright © Cambridge University Press 1993

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References

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