Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915536490725376 |
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| author | Radchenko, Danylo Sun, Qihang |
| author_facet | Radchenko, Danylo Sun, Qihang |
| contents | We give a construction of radial Fourier interpolation formulas in dimensions 3 and 4 using Maass--Poincaré type series. As a corollary we obtain explicit formulas for the basis functions of these interpolation formulas in terms of what we call real-variable Kloosterman sums, which were previously introduced by Stoller. We also improve the bounds on the corresponding basis functions $a_{n,d}(x)$, $d=3,4$, for fixed $x$, in terms of the index $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04873 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums Radchenko, Danylo Sun, Qihang Number Theory Classical Analysis and ODEs 42B99, 11F03, 11F37, 11L05 We give a construction of radial Fourier interpolation formulas in dimensions 3 and 4 using Maass--Poincaré type series. As a corollary we obtain explicit formulas for the basis functions of these interpolation formulas in terms of what we call real-variable Kloosterman sums, which were previously introduced by Stoller. We also improve the bounds on the corresponding basis functions $a_{n,d}(x)$, $d=3,4$, for fixed $x$, in terms of the index $n$. |
| title | Fourier interpolation in dimensions 3 and 4 and real-variable Kloosterman sums |
| topic | Number Theory Classical Analysis and ODEs 42B99, 11F03, 11F37, 11L05 |
| url | https://arxiv.org/abs/2510.04873 |