Asymptotic analysis of oscillatory integrals via the Newton polyhedra of the phase and the amplitude

Details Asymptotic analysis of oscillatory integrals via the Newton polyhedra of the phase and the amplitude Asymptotic analysis of oscillatory integrals via the Newton polyhedra of the phase and the amplitude

2012-03-05

arxiv.org/abs/1203.0808v1

Mathematics

Classical Analysis and ODEs

36 pages

Scientific paper

The asymptotic behavior at infinity of oscillatory integrals is in detail investigated by using the Newton polyhedra of the phase and the amplitude. We are especially interested in the case that the amplitude has a zero at a critical point of the phase. The properties of poles of local zeta functions, which are closely related to the behavior of oscillatory integrals, are also studied under the associated situation.

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