On series Σc k f(kx) and Khinchin’s conjecture

István Berkes, Michel Weber

Research output: Contribution to journalArticlepeer-review


We prove the optimality of a criterion of Koksma (1953) in Khinchin’s conjecture on strong uniform distribution. This verifies a claim of Bourgain (1988) and leads also to a near optimal a.e. convergence condition for series Σ ∞ k=1 c k f(kx) with f ∈ L 2. Finally, we show that under mild regularity conditions on the Fourier coefficients of f, the Khinchin conjecture is valid assuming only f ∈ L 2.
Original languageEnglish
Pages (from-to)593-609
JournalIsrael Journal of Mathematics
Issue number2
Publication statusPublished - Feb 2014

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


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