Fourier decay of measures supported on sets of numbers with consecutive partial quotients belonging to a given set

2025/03/21 by Robert Fraser, Fraser, Robert
Mathematics · #11J83 #28A80 #42A99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2503.17277

openalex publication_date 2025/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider measures supported on sets of irrational numbers possessing many consecutive partial quotients satisfying a condition based on the previous partial quotients. We show that under mild assumptions, such sets will always support measures whose Fourier transform decays to zero.

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