Harmonic analysis and additive combinatorics

An uncertainty principle for cyclic groups of prime order

Terence Tao · Human-authored comparison

7 pages4 claims indexed18 referencesManuscript 2004-07-22

The proposed argument

A cyclotomic-integer lemma controls polynomial values at roots of unity modulo p. Dividing a Fourier minor by its Vandermonde factors and evaluating derivatives proves that every square minor is nonzero. Invertibility then gives the support-sum bound and its converse, followed by sparse-polynomial and sumset consequences.

Human-authored control; withheld identifying front matter. Model conclusions and curator source checks remain separate from human mathematical grades.

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    Your independent assessment

    Trace the cyclotomic lemma, Fourier-minor argument, exact-support converse, and the applications. Distinguish proof defects from exposition and imported prerequisites.

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