Kuznecov remainders and generic metrics
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908442226065408 |
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| author | Kaloshin, Vadim Wyman, Emmett L. Xi, Yakun |
| author_facet | Kaloshin, Vadim Wyman, Emmett L. Xi, Yakun |
| contents | We obtain improved remainder estimates in the Kuznecov sum formula for period integrals of Laplace eigenfunctions on a Riemannian manifold $M$. Building upon the two-term asymptotic expansion established in [arXiv:2204.13525], we prove that for a Baire-generic class of metrics, the oscillatory second term in the Kuznecov formula can be eliminated, yielding an improved remainder estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06887 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kuznecov remainders and generic metrics Kaloshin, Vadim Wyman, Emmett L. Xi, Yakun Analysis of PDEs Differential Geometry Spectral Theory We obtain improved remainder estimates in the Kuznecov sum formula for period integrals of Laplace eigenfunctions on a Riemannian manifold $M$. Building upon the two-term asymptotic expansion established in [arXiv:2204.13525], we prove that for a Baire-generic class of metrics, the oscillatory second term in the Kuznecov formula can be eliminated, yielding an improved remainder estimate. |
| title | Kuznecov remainders and generic metrics |
| topic | Analysis of PDEs Differential Geometry Spectral Theory |
| url | https://arxiv.org/abs/2507.06887 |