An effective van der Corput-type method in higher dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912757177122816 |
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| author | Xu, Shaozhen |
| author_facet | Xu, Shaozhen |
| contents | Using the birational map between a smooth toric variety (adapted to the phase function of the oscillatory integral) and $\mathbb{R}^n\textbackslash\{0\}$, we can effectively carry out the van der Corput-type analysis in higher dimensions. This allows us to give an elegant derivation of the leading term in Varchenko's asymptotic expansion \cite{Var76}. We expect that this observation may have further applications to other problems involving oscillatory integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_19922 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An effective van der Corput-type method in higher dimensions Xu, Shaozhen Classical Analysis and ODEs Algebraic Geometry Using the birational map between a smooth toric variety (adapted to the phase function of the oscillatory integral) and $\mathbb{R}^n\textbackslash\{0\}$, we can effectively carry out the van der Corput-type analysis in higher dimensions. This allows us to give an elegant derivation of the leading term in Varchenko's asymptotic expansion \cite{Var76}. We expect that this observation may have further applications to other problems involving oscillatory integrals. |
| title | An effective van der Corput-type method in higher dimensions |
| topic | Classical Analysis and ODEs Algebraic Geometry |
| url | https://arxiv.org/abs/2511.19922 |