A converse to a theorem of Gauss on Gauss sums
| Autor: | Bober, Jonathan W., Goldmakher, Leo |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 4 pages. Comments very welcome! |
| Databáze: | arXiv |
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