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Bibliographic Details
Main Authors: Bober, Jonathan W., Goldmakher, Leo
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2407.16937
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Table of 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.