| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
(1) We study toric blowing-ups related to Newton polyhedra. Using the blowing-ups, we locally represent the zero variety of smooth functions in simplified forms in two-dimensional cases. (2) We investigate the asymptotic behavior of oscillatory integrals with smooth phases in two dimensions. We have very interesting results such as log terms appearing in asymptotic limit of oscillatory integrals. (3) We show that local zeta functions can not be analytically continued as meromorphic functions across some point in some two dimensional smooth setting. In more general case, the region to which local zeta functions can be analytically continued as meromorphic functions are estimated by some geometrical information of Newton polyhedra.
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