Pólya's conjecture for Dirichlet eigenvalues of annuli
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910015891177472 |
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| author | Filonov, Nikolay Levitin, Michael Polterovich, Iosif Sher, David A. |
| author_facet | Filonov, Nikolay Levitin, Michael Polterovich, Iosif Sher, David A. |
| contents | We prove Pólya's conjecture for the eigenvalues of the Dirichlet Laplacian on annular domains. Our approach builds upon and extends the methods we previously developed for disks and balls. It combines variational bounds, estimates of Bessel phase functions, refined lattice point counting techniques, and a rigorous computer-assisted analysis. As a by-product, we also derive a two-term upper bound for the Dirichlet eigenvalue counting function of the disk, improving upon Pólya's original estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pólya's conjecture for Dirichlet eigenvalues of annuli Filonov, Nikolay Levitin, Michael Polterovich, Iosif Sher, David A. Spectral Theory Number Theory 35P15 (Primary) 35P20, 33C10, 11P21, 65G20 (Secondary) We prove Pólya's conjecture for the eigenvalues of the Dirichlet Laplacian on annular domains. Our approach builds upon and extends the methods we previously developed for disks and balls. It combines variational bounds, estimates of Bessel phase functions, refined lattice point counting techniques, and a rigorous computer-assisted analysis. As a by-product, we also derive a two-term upper bound for the Dirichlet eigenvalue counting function of the disk, improving upon Pólya's original estimate. |
| title | Pólya's conjecture for Dirichlet eigenvalues of annuli |
| topic | Spectral Theory Number Theory 35P15 (Primary) 35P20, 33C10, 11P21, 65G20 (Secondary) |
| url | https://arxiv.org/abs/2505.21737 |