2021-12-08T04:32:48Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000399482021-03-02T02:42:20ZToric Resolution of Singularities in a Certain Class of C∞ Functions and Asymptotic Analysis of Oscillatory IntegralsKamimoto, Joe92351Nose, Toshihiro92352415Oscillatory integralsoscillation index and its multiplicitylocal zeta functiontoric resolutionthe classes εˆ[P](U) and εˆ(U)asymptotic expansionNewton polyhedraIn a seminal work of A. N. Varchenko, the behavior at infinity of oscillatory integrals with real analytic phase is precisely investigated by using the theory of toric varieties based on the geometry of the Newton polyhedron of the phase. The purpose of this paper is to generalize his results to the case that the phase is contained in a certain class of C∞ functions. The key in our analysis is a toric resolution of singularities in the above class of C∞ functions. 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.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2016-02-25application/pdfJournal of mathematical sciences, the University of Tokyo223425485AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/39948/files/jms230203.pdfeng