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  • Autor
    • Berkes, István
    • Weber, Michel
  • TitelOn series \(∑ c_k f (kx)\) and Khinchin’s conjecture
  • Volltext
  • LicenceCC BY
  • ZugriffsrechteCC-BY
  • Download Statistik18
  • Peer ReviewNein
  • AbstractWe 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 \(∑^{∞}_{k=1} c_k f (kx)\) with \(f ∈ L^2\) . Finally we show that under mild regularity condi- tions on the Fourier coefficients of f , the Khinchin conjecture is valid assuming only \(f ∈ L^2\) .