- Autor
- Berkes, István
- Weber, Michel
- TitelOn series \(∑ c_k f (kx)\) and Khinchin’s conjecture
- Datei
- Erschienen inIsrael Journal of Mathematics
- Band201
- Erscheinungsjahr2014
- Heft2
- Seiten593-609
- LicenceCC BY
- Download Statistik2087
- 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 conditions on the Fourier coefficients of \(f\) , the Khinchin conjecture is valid assuming only \(f ∈ L^2\) .
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