Projects per year
Abstract
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 language | English |
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Pages (from-to) | 593-609 |
Journal | Israel Journal of Mathematics |
Volume | 201 |
Issue number | 2 |
DOIs | |
Publication status | Published - Feb 2014 |
Fields of Expertise
- Information, Communication & Computing
Treatment code (Nähere Zuordnung)
- Basic - Fundamental (Grundlagenforschung)
Projects
- 1 Finished
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Analytic Combinatorics: Analytic Combinatorics and Probabilistic Number Theory
Wagner, S., Madritsch, M., Aistleitner, C., Barat, G., Thuswaldner, J., Grabner, P., Van De Woestijne, C. E., Heuberger, C., Brauchart, J., Berkes, I., Filipin, A., Zeiner, M. & Tichy, R.
1/01/06 → 31/07/12
Project: Research project