Fourier decay of measures supported on sets of numbers with consecutive partial quotients belonging to a given set
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912286305681408 |
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| author | Fraser, Robert |
| author_facet | Fraser, Robert |
| contents | We consider measures supported on sets of irrational numbers possessing many consecutive partial quotients satisfying a condition based on the previous partial quotients. We show that under mild assumptions, such sets will always support measures whose Fourier transform decays to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fourier decay of measures supported on sets of numbers with consecutive partial quotients belonging to a given set Fraser, Robert Classical Analysis and ODEs Number Theory 42A99, 28A80, 11J83 We consider measures supported on sets of irrational numbers possessing many consecutive partial quotients satisfying a condition based on the previous partial quotients. We show that under mild assumptions, such sets will always support measures whose Fourier transform decays to zero. |
| title | Fourier decay of measures supported on sets of numbers with consecutive partial quotients belonging to a given set |
| topic | Classical Analysis and ODEs Number Theory 42A99, 28A80, 11J83 |
| url | https://arxiv.org/abs/2503.17277 |