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Diophantine approximation on the parabola with non-monotonic approximation functions
Published online by Cambridge University Press: 15 January 2019
Abstract
We show that the parabola is of strong Khintchine type for convergence, which is the first result of its kind for curves. Moreover, Jarník type theorems are established in both the simultaneous and the dual settings, without monotonicity on the approximation function. To achieve the above, we prove a new counting result for the number of rational points with fixed denominators lying close to the parabola, which uses Burgess’s bound on short character sums.
MSC classification
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 168 , Issue 3 , May 2020 , pp. 535 - 542
- Copyright
- Copyright © Cambridge Philosophical Society 2019
Footnotes
Supported by the UNR VPRI startup grant 1201-121-2479.
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