A converse to a theorem of Gauss on Gauss sums
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 con...
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| Zusammenfassung: | 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. |
|---|---|
| DOI: | 10.48550/arxiv.2407.16937 |