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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.16937 |
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| _version_ | 1866929434798325760 |
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| author | Bober, Jonathan W. Goldmakher, Leo |
| author_facet | Bober, Jonathan W. Goldmakher, Leo |
| contents | In this note we prove (under mild hypotheses) that $f$ is a nontrivial character of $\mathbb{F}_p$ if and only if the Fourier transform of $f$ has magnitude 1 somewhere in $\mathbb{F}_p^\times$. This implies a converse to a theorem of Gauss on the magnitude of the Gauss sum, in addition to other consequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16937 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A converse to a theorem of Gauss on Gauss sums Bober, Jonathan W. Goldmakher, Leo Number Theory Representation Theory 11L05 (Primary) 11T24, 20C15 (Secondary) In this note we prove (under mild hypotheses) that $f$ is a nontrivial character of $\mathbb{F}_p$ if and only if the Fourier transform of $f$ has magnitude 1 somewhere in $\mathbb{F}_p^\times$. This implies a converse to a theorem of Gauss on the magnitude of the Gauss sum, in addition to other consequences. |
| title | A converse to a theorem of Gauss on Gauss sums |
| topic | Number Theory Representation Theory 11L05 (Primary) 11T24, 20C15 (Secondary) |
| url | https://arxiv.org/abs/2407.16937 |